Consider the following matrix. A=[} 1&-1 -3&2 ] Choose the correct description of A. Find A^-1 if it exists. A is nonsingular That is, it has an inverse. A^-1=square A is singular. That is, its inverse doesn't exist.

Question

Consider the following matrix. A=[} 1&-1 -3&2 ] Choose the correct description of A. Find A^-1 if it exists. A is nonsingular That is, it has an inverse. A^-1=square A is singular. That is, its inverse doesn't exist.

Answer 1

To determine whether the matrix

is singular or nonsingular, we need to calculate its determinant. If the determinant is nonzero, then the matrix is nonsingular and has an inverse. If the determinant is zero, then the matrix is singular and does not have an inverse.The matrix

is given by:

The determinant of

is calculated as follows:

Since the determinant of

is

, which is nonzero, the matrix

is nonsingular and has an inverse.To find the inverse of

, we use the formula for the inverse of a 2x2 matrix:

For the matrix

, the elements are:

Substituting these values into the formula, we get:

Therefore, the inverse of

is:

So, the correct description of

is:

And the inverse of

is:

Problemas

Consider the following matrix. A=[} 1&-1 -3&2 ] Choose the correct description of A. Find A^-1 if it exists. A is nonsingular That is, it has an inverse. A^-1=square A is singular. That is, its inverse doesn't exist.

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