Inverses of Matrices - Pre-Calculus

Note the first and the last columns are equal.

Therefore, when we try to find the determinant using the following formula we get the determinant equaling 0:

This means simply, that the matrix does not have an inverse.

For a 2x2 matrix

the inverse can be found by

Because the determinant is equal to zero in this problem, or

,

the inverse does not exist.

There are a couple of ways to do this. I will use the determinant method.

First we need to find the determinant of this matrix, which is

for a matrix in the form:

.

Substituting in our values we find the determinant to be:

Now one formula for finding the inverse of the matrix is

.

We use the inverse of a 2x2 matrix formula to determine the answer. Given a matrix

it's inverse is given by the formula:

First we define the determinant of our matrix:

Then,

This matrix has no inverse because the columns are not linearly independent. This means if you row reduce to try to compute the inverse, one of the rows will have only zeros, which means there is no inverse.

By writing the augmented matrix , and reducing the left side to the identity matrix, we can implement the same operations onto the right side, and we arrive at , with the right side representing the inverse of the original matrix.

Note the first and the last columns are equal.

Therefore, when we try to find the determinant using the following formula we get the determinant equaling 0:

This means simply, that the matrix does not have an inverse.

For a 2x2 matrix

the inverse can be found by

Because the determinant is equal to zero in this problem, or

,

the inverse does not exist.

There are a couple of ways to do this. I will use the determinant method.

First we need to find the determinant of this matrix, which is

for a matrix in the form:

.

Substituting in our values we find the determinant to be:

Now one formula for finding the inverse of the matrix is

.

We use the inverse of a 2x2 matrix formula to determine the answer. Given a matrix

it's inverse is given by the formula:

First we define the determinant of our matrix:

Then,

This matrix has no inverse because the columns are not linearly independent. This means if you row reduce to try to compute the inverse, one of the rows will have only zeros, which means there is no inverse.

By writing the augmented matrix , and reducing the left side to the identity matrix, we can implement the same operations onto the right side, and we arrive at , with the right side representing the inverse of the original matrix.

By definition, an inverse matrix is the matrix B that you would need to multiply matrix A by to get the identity. Since the identity matrix yields whatever matrix it is being multiplied by, the answer is the identity itself.

By definition, an inverse matrix is the matrix B that you would need to multiply matrix A by to get the identity. Since the identity matrix yields whatever matrix it is being multiplied by, the answer is the identity itself.

Note the first and the last columns are equal.

Therefore, when we try to find the determinant using the following formula we get the determinant equaling 0:

This means simply, that the matrix does not have an inverse.

For a 2x2 matrix

the inverse can be found by

Because the determinant is equal to zero in this problem, or

,

the inverse does not exist.

There are a couple of ways to do this. I will use the determinant method.

First we need to find the determinant of this matrix, which is

for a matrix in the form:

.

Substituting in our values we find the determinant to be:

Now one formula for finding the inverse of the matrix is

.

We use the inverse of a 2x2 matrix formula to determine the answer. Given a matrix

it's inverse is given by the formula:

First we define the determinant of our matrix:

Then,

This matrix has no inverse because the columns are not linearly independent. This means if you row reduce to try to compute the inverse, one of the rows will have only zeros, which means there is no inverse.