COMEDK20269 May 2026Morning ShiftMathematicsMatricesActual

Given A = pmatrix 1 & 2 2 & 3 pmatrix and f(x) = x^2 - 2x - 3 then f(A) is:

Options

ANull matrix
BSymmetric Matrix
CSkew symmetric matrix
DIdentity matrix

Correct answer

B. Symmetric Matrix

Step-by-step solution

Given A = pmatrix 1 & 2 2 & 3 pmatrix and f(x) = x^2 - 2x - 3 f(A) = A^2 - 2A - 3I A^2 = pmatrix 1 & 2 2 & 3 pmatrix pmatrix 1 & 2 2 & 3 pmatrix = pmatrix 5 & 8 8 & 13 pmatrix f(A) = pmatrix 5 & 8 8 & 13 pmatrix - pmatrix 2 & 4 4 & 6 pmatrix - pmatrix 3 & 0 0 & 3 pmatrix f(A) = pmatrix 0 & 4 4 & 4 pmatrix Since (f(A))^T = f(A) , the resulting matrix is a symmetric matrix. Answer: Symmetric Matrix

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