If find A–1. Using A–1, solve the system of linear equations x – 2y = 10, 2x – y – z = 8, –2y + z = 7.


We have,

We have to find A-1 and


Firstly, we find |A|


Expanding |A| along C1, we get




= (-1 + 2) + 2 (0) + 0


= 1


Now, we have to find adj A and for that we have to find co-factors:













Now, the system of linear equation is


x – 2y = 10


2x – y – z = 8


-2y + z = 7


We know that, AX = B


Here,


and we can see that this matrix is the transpose of the given matrix. So, transpose of A-1 is



X = A-1B





x = 0, y = -5 and z = -3


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