Final answer:
To make the matrix singular when p = 9, we must find the value of k that sets the determinant of the matrix to zero. By substituting p = 9 into the determinant formula of the given matrix and solving the resulting equation for k, we will find the value that makes the matrix singular.
Step-by-step explanation:
To determine the value of k that makes the matrix singular when p = 9, we must understand that a singular matrix is one for which the determinant is zero. Typically, the determinant of a matrix A is calculated depending on its size, but for a 2x2 matrix, the determinant is calculated using the formula det(A) = ad - bc where a, b, c, and d are the elements of the matrix. If we are given a specific matrix with elements that include p and k, then we would substitute p = 9 into the matrix and then solve the equation det(A) = 0 for the variable k to find the value that renders the matrix singular.
For example, for a matrix A with the form:
| p k |
| k p |
The determinant of A is (p*p) - (k*k) = p2 - k2. Substituting p = 9, we get:
det(A) = 92 - k2 = 81 - k2
To find the value of k that makes det(A) = 0, solve for k in:
81 - k2 = 0
Thus we get k2 = 81, and k would be plus or minus 9.