‫بسم هللا الرحمن الرحيم‬
Majmaah University
College of Engineering
Math107
HW
Q1: Solve the following system by Guass-Jordan elimination method and
describe the type of solution
a)
x  y  2z  8
 x  2 y  3z  1
3 x  7 y  4 z  10
b)
5 x-2 y  6 z  0
-2 x  y  3z  1
c)
x  2 y  z  4w  1
x  3 y  7 z  2w  2
x  12 y  11z  16 w  5
Q2: Solve part 1 in Q1 using the inverse method
Q3: For which values of K will the following system have
1)No solution 2) infinitely many solution 3) unique solution (Exactly one
solution )
a)
x  2y  3
2 x  ( K 2  3) y  K  7
b)
x  y  3z  4
3x  y  5 z  2
4 x  y  ( K 2  14) z  k  2
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‫بسم هللا الرحمن الرحيم‬
Q4: Let B be a square matrix prove that
1) B.B T and B  B T are symmetric matrices
2) B  B T is skew symmetric matrix
Note that 1) if Wnxn  W T nxn then W is called symmetric matrix
2) if Wnxn   W T nxn then W is called skew symmetric matrix
END
Dr. Mukhtar Salah
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