# Problem Sheet #6 ClassID: _____ Name: _________________________ Hmk. 6 Score _________ ```Problem Sheet #6 (2.2-2.4)
ClassID: _____ Name: _________________________ Hmk. 6 Score _________
Math 1090 – 001 Spring 2013
Instructor: Katrina Johnson
Complete each problem. No credit will be given without supporting work.
1. Using these matrices, perform the following calculations (or state that it’s not possible):
⎡ 1 −2 ⎤
A = ⎢
⎥
⎣−1 0 ⎦
⎡5 3⎤
B = ⎢
⎥
⎣4 1 ⎦
a) AB
€
⎡ 3 −2 2 ⎤
C = ⎢
⎥
⎣−1 2 1 ⎦
⎡−1⎤
X = [ 4 −3] Y = ⎢ ⎥
⎣ 2 ⎦
d) CA
€
€
€
e) BC
b) XY
c) YX
⎧ x + 2y − z = 5
⎪
2. ⎨ −x + 3z = −1
⎪
⎩ z + y − x = 4
a) Write the system of equations as an augmented matrix.
€
b) Write the system of equations as a matrix equation.
€
3. Use Gauss-Jordan Elimination to solve the system of equations.
⎧ 3x − y = 1
⎪
⎨2x − y + z = 0
⎪
⎩ x + z = −1
€
4. Find the inverse of the matrix, or state that the inverse does not exist.
⎡1 0 1 ⎤
⎢
⎥
M = ⎢3 −1 0 ⎥
⎢⎣2 −1 1 ⎥⎦
€
5. Solve the system of linear equations using an inverse matrix.
⎧2x + y = −2
⎨
⎩ 3x − y = 2
€
```