Final answer:
The value of k for which matrix a is singular can be determined by setting up and solving the equation det(A) = 0, where A includes the variable p and the unknown k.
Step-by-step explanation:
If p = 5, to determine the value of k for which the matrix a is singular, we must assume that we have a matrix where the value of p affects its determinants, such as a square matrix with an element or elements that include the variable p. A matrix is said to be singular if its determinant is equal to zero. Without the specific matrix, we would apply the general rule that for any square matrix A, if det(A) = 0, then A is singular.
To solve for k, the student must set up the determinant of the matrix involving p and k, and then solve the equation det(A) = 0 for k. For example, if we had a 2x2 matrix:
[[p, k],
[3, 4]],
We would calculate its determinant as p*4 - k*3. If p = 5, we'd set 5*4 - 3k = 0 and solve for k to find the value that makes the matrix singular