If for a square matrix A, A2 3A + I = O and A 1 = xA + yI, then thevalue of x + y is :
Question
If for a square matrix A,
A^2 - 3A + I = O
and
A^{-1} = xA + yI,
then the value of x + y is :
Solution
The question seems to be incomplete or incorrectly formatted. However, I'll try to provide a general solution based on the given information.
Given that A^2 - 3A + I = O, where A is a square matrix, I is the identity matrix, and O is the zero matrix.
Also given that A * 1 = xA + yI, which simplifies to A = xA + yI.
From this, we can infer that x = 1 (since xA should be equal to A) and y = 0 (since there is no identity matrix on the left side of the equation).
Therefore, the value of x + y would be 1 + 0 = 1.
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