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Find the matrix A such that

1 0

−1 3
A =

−1 −8

2 11
.
Hint: Let
A =

a b

c d


A=

  • Math -

    | 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

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