Find the matrix A such that
1 0
−1 3
A =
−1 −8
2 11
.
Hint: Let
A =
a b
c d
A=
| 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
Sure, let's solve this with a hint.
Using the given hint, we have A =
a b
c d
Now, comparing the matrix elements to the given matrix, we have:
a = 1, b = 0, c = -1, d = 3
So, our matrix A is:
A =
1 0
-1 3
To find the matrix A, we can match the corresponding elements from the given matrix and the matrix representation of A.
So, we have:
a = 1, b = 0, c = -1, d = 3
Therefore, the matrix A is:
A =
1 0
-1 3
-1 -8
2 11
To find the matrix A, we need to determine the values of a, b, c, and d.
Looking at the provided hint, we can set up the equations by comparing the corresponding elements from the given matrix and the matrix A:
For the top-left element:
1 = a
For the top-right element:
0 = b
For the bottom-left element:
-1 = c
For the bottom-right element:
3 = d
Therefore, we have determined all the values:
a = 1
b = 0
c = -1
d = 3
Plugging these values into the matrix A:
A =
1 0
-1 3