Find the matrix A such that

Question

1 0

−1 3
A =

−1 −8

2 11
.
Hint: Let
A =

a b

c d

A=

Answer 1

| 1 0 | | a b | |-1 -8 |
|-1 3 | | c d | | 2 11 |

so
1 a + 0 c = -1 ---> a = -1

1 b + 0 d = -8 ----> b = -8

-1 a + 3 c = 2
but a = -1
1 + 3 c = 2
c = 1/3

-1 b + 3 d = 11
but b = -8
8 + 3 d = 11
3 d = 3
d = 1