Consider the matrix A =k −k 3 00 k + 1 1 kk −3 5 k − 50 −3 0 −k.(a) Find det(A).(b) Find all values of k such that A is singular.
Question
Solution 1
(a) To find the determinant of a 4x4 matrix, we can use the method of cofactor expansion. However, in this case, the matrix has a lot of zeros, which simplifies the process. We can expand along the first row:
det(A) = k * det(3x3 submatrix) - (-k) * det(3x3 submatrix) + 3 * det(3x3 submatrix) + 0
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