# 04-L-05.10.2016

```05.10.2016
v2.0
Applications
lin&eacute;aires
Alg&egrave;bre Lin&eacute;aire 2016
1
Transformations lin&eacute;aires du plan
✓
✓
0
1
◆
0
0
◆
✓
✓
Alg&egrave;bre Lin&eacute;aire 2016
1
1
1
0
◆
◆
2
Projection sur l’axe horizontale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
◆
3
Projection sur l’axe horizontale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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3
Projection sur l’axe horizontale
✓
x
y
◆
7!
✓
1
0
0
0
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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3
Projection sur l’axe verticale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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4
Projection sur l’axe verticale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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4
Projection sur l’axe verticale
✓
x
y
◆
7!
✓
0
0
0
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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4
Projection sur la droite y=x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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5
Projection sur la droite y=x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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5
Projection sur la droite y=x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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5
Projection sur la droite y=x
✓
x
y
◆
1
7
!
2
✓
1
1
1
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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5
Contraction
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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6
Contraction
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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6
Contraction
✓
x
y
◆
7!
✓
r
0
0
r
◆✓
x
y
◆
=
0r1
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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6
Dilation
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
◆
7
Dilation
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
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0
0
◆
7
Dilation
✓
x
y
◆
7!
✓
r
0
0
r
◆✓
x
y
◆
=
1r
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
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0
0
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7
R&eacute;flexion par (0,0)
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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8
R&eacute;flexion par (0,0)
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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8
R&eacute;flexion par (0,0)
✓
x
y
◆
7!
✓
1
0
0
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
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0
0
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8
R&eacute;flexion par rapport &agrave; la droite x=y
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
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0
0
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9
R&eacute;flexion par rapport &agrave; la droite x=y
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
◆
9
R&eacute;flexion par rapport &agrave; la droite x=y
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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9
R&eacute;flexion par rapport &agrave; la droite x=y
✓
x
y
◆
7!
✓
0
1
1
0
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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9
R&eacute;flexion par rapport &agrave; une droite quelconque
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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10
ax
+b
y=
0
R&eacute;flexion par rapport &agrave; une droite quelconque
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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10
ax
+b
y=
0
R&eacute;flexion par rapport &agrave; une droite quelconque
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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10
7!
1
a 2 + b2
✓
b
2
2
a
2ab
a2
2ab
b2
◆✓
x
y
◆
+b
x
y
◆
ax
✓
y=
0
R&eacute;flexion par rapport &agrave; une droite quelconque
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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10
R&eacute;flexion par rapport &agrave; la droite y=-x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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11
R&eacute;flexion par rapport &agrave; la droite y=-x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
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0
0
◆
11
R&eacute;flexion par rapport &agrave; la droite y=-x
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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11
R&eacute;flexion par rapport &agrave; la droite y=-x
✓
x
y
◆
7!
✓
0
1
1
0
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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11
R&eacute;flexion par rapport &agrave; l’axe horizontal
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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12
R&eacute;flexion par rapport &agrave; l’axe horizontal
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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12
R&eacute;flexion par rapport &agrave; l’axe horizontal
✓
x
y
◆
7!
✓
1
0
0
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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12
R&eacute;flexion par rapport &agrave; l’axe vertical
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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13
R&eacute;flexion par rapport &agrave; l’axe vertical
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
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13
R&eacute;flexion par rapport &agrave; l’axe vertical
✓
x
y
◆
7!
✓
1
0
0
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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13
Rotation d’angle 45 degr&eacute;s
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=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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14
Rotation d’angle 45 degr&eacute;s
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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14
Rotation d’angle 45 degr&eacute;s
✓
x
y
◆
1
7 p
!
2
✓
1
1
1
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
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1
1
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0
1
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0
0
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14
Rotation d’angle quelconque
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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15
Rotation d’angle quelconque
=
'
Alg&egrave;bre Lin&eacute;aire 2016
✓
=
✓
=
✓
=
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
15
Rotation d’angle quelconque
✓
x
y
◆
7!
✓
cos(')
sin(')
sin(')
cos(')
◆✓
x
y
=
◆
'
Alg&egrave;bre Lin&eacute;aire 2016
✓
=
✓
=
✓
=
✓
1
0
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1
1
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0
1
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0
0
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15
Transvection horizontale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
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0
1
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0
0
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16
Transvection horizontale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
16
Transvection horizontale
✓
x
y
◆
7!
✓
1
0
a
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
16
Transvection verticale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
17
Transvection verticale
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
17
Transvection verticale
✓
x
y
◆
7!
✓
1
a
0
1
◆✓
x
y
◆
=
=
✓
=
✓
=
Alg&egrave;bre Lin&eacute;aire 2016
✓
✓
1
0
◆
1
1
◆
0
1
◆
0
0
◆
17
```