I got the four equations as

a - b = -5

c -d = 7

4b = -4

4d = 12

solving these I get A as

A = [-6 -1]

A = [10 3]

I got the four equations as

a - b = -5

c -d = 7

4b = -4

4d = 12

solving these I get A as

A = [-6 -1]

A = [10 3]

a - b = -5

c -d = 7

4b = -4

4d = 12

solving these I get A as

A = [-6 -1]

A = [10 3]

- stapel_eliz
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littlebu wrote:I got the four equations as

a - b = -5

c -d = 7

4b = -4

4d = 12

Excellent! That's exactly right. Then:

. . . . .4b = -4, so b = -1

. . . . .a - (-1) = -5, so a = -6

. . . . .4d = 12, so d = 3

. . . . .c - (3) = 7, so c = 10

And then you can quickly check:

. . . . .

Since the matrices multiply to the desired result, this confirms that your answer is correct. Good work!