If A= [ array cc 2-k & 2 1 & 3-k array ] is a singular matrix, then the value of 5 k-k^2 is

Step-by-step solution

A matrix A is singular if its determinant is zero, so (A) = 0 . Given A = bmatrix 2-k & 2 1 & 3-k bmatrix , the determinant is calculated as: (A) = (2-k)(3-k) - (2)(1) = 0 Expanding the expression: 6 - 2k - 3k + k^2 - 2 = 0 k^2 - 5k + 4 = 0 Rearranging the terms to find the value of 5k - k^2 : k^2 - 5k = -4 Multiplying by -1 gives: 5k - k^2 = 4 Answer: 4