Given that k is a real number and that A = ((1+k k)(k 1-k)) find the exact values of k for which A is a singular matrix.

okay so A is a 2x2 matrix.for it to be singular its determinate has to equal 0.a 2x2 matrix's determinate is equal to m1,1m2,2 - m1,2m2,1for this example:det(A) = (1+k)(1-k) - (k)(k) = 0multiplying out the brackets(1+k)(1-k) becomes 1-k+k-k2 = 1-k2(k)(k) becomes k2so det(A)= 1-k2-k2 = 1-2k2 = 0solving for k1=2k21/2 = k2so k = +/-SQRT(1/2)

KY
Answered by Kieran Y. Further Mathematics tutor

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