Question

Which expression represents the inverse of the matrix below?

[1 3 -1; 2 -2 -3; 1 1 -1; -2 -3 1]
a) [2 1 -2; -3 1 -3; 1 -3 1]
b) [1 -2 1; 3 1 -3; -1 -3 2]
c) [-2 1 -2; 3 -1 3; -1 3 -1]
d) [1 3 2; -3 1 3; 1 -2 -1]

Answer 1

The inverse of the given matrix cannot be found because it is not a square matrix. None of the options provided are correct. d) None of the above

Step-by-step explanation:

Since the given matrix has dimensions 4x3, it means that its inverse cannot be found because it is not a square matrix. Therefore, none of the options provided represent the inverse of the given matrix. The correct answer is:

d) None of the above

Answer 2

Inverse of the matrix is [-2 1 -2; 3 -1 3; -1 3 -1] (option c)

Step-by-step explanation:

The inverse of a matrix A, denoted as A⁻¹, is such that when multiplied by the original matrix A, it results in the identity matrix. To determine the inverse of the given matrix, calculate its inverse and verify the product with the original matrix to confirm if it yields the identity matrix. Among the options provided, the matrix represented in option c) [-2 1 -2; 3 -1 3; -1 3 -1] is the inverse matrix. (option c)

Matrix inversion involves a series of calculations, including determinant computation, adjoint matrix determination, and scalar multiplication, to obtain the inverse matrix. This inverse matrix, when multiplied by the original matrix, should yield the identity matrix.

Understanding matrix inversion is essential in various fields, especially in solving systems of linear equations, transformations, and other mathematical applications. The inverse matrix allows for solving equations involving matrices and is a fundamental concept in linear algebra.