Question

Find a and b ax-b ,-1

Answer 1

Let X=[xy], then the first equation can be written, in matrix multiplication, as

[2−3][xy]=[−1]

Similarly, the second equation can be written as

[−55][xy]=[20]

By combining these two equations as a system, they can be written as

[2−5−35][xy]AX=[−120]=B

Now, if the above A has an inverse, then both sides can be left-multiplied by A−1 to get

AXA−1AXI2XX[xy]=B=A−1B=A−1B=A−1B=[2−5−35]−1[−120]