Express the system of linear equations in the form AX = b, where A is a 3

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Express the system of linear equations

3x - y + 4z = 13 5x + y 3z = 5 x = y + z = - 3

in the form AX = b, where A is a 3 × 3 matrix and X, b are appropriate column matrices.

(a) Find adj A, |A| and A–1 and hence solve the system of equations.

(b) Find a matrix Y which satisfies the equation

AYA = 22A + 2A

(c) Find a matrix Z which satisfies the equation

AZ = 4413 A + AA -

where I3 is the 3 × 3 identity matrix.

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