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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 m_1,1m_2,2 - m_1,2m_2,1for 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)

Answered by Kieran Y. • Further Mathematics tutor

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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.

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