# Common Core: High School - Algebra : Use Matrix Inverse to Solve System of Linear Equations: CCSS.Math.Content.HSA-REI.C.9

## Example Questions

### Example Question #1 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes

No

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , , , and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #2 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

Yes

No

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #2 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

Yes

No

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #4 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #5 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

Yes

No

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #6 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

Yes

No

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #7 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #8 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes

No

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #9 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

### Example Question #10 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

No

Yes