Question

Find the inverse of the matrix, if it exists. Verify your answer. (If an answer does not exist, enter DNE in any cell of the matrix.) 1 1 −1 1 5 1 1 0 5 1 0 1 5 −1 −1 4

Answer 1

Finding the inverse of a matrix involves reducing an augmented matrix with the identity to RREF; if the identity is achieved, the other side is the inverse, verified by multiplication with the original.

Step-by-step explanation:

The question asks to find the inverse of a matrix, if it exists. The process involves several steps including creating an augmented matrix with the identity matrix, applying row operations to reduce it to row-echelon form, then reducing to reduced row-echelon form (RREF). If the left side of the augmented matrix can be reduced to the identity matrix through these operations, its right side will then represent the inverse of the original matrix. To verify the answer, we multiply the original matrix by the obtained inverse matrix. If the product is the identity matrix, the calculated inverse is correct.