# Linear Algebra : Matrix-Vector Product

## Example Questions

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Multiply

Explanation:

Multiply:

Explanation:

### Example Question #3 : Matrix Vector Product

Compute AB.

Explanation:

Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 2x3 matrix:

### Example Question #2 : Matrix Vector Product

Compute AB

Explanation:

Because the number of columns in matrix A and the number of rows in matrix B are equal, we know that product AB does in fact exist. Matrix AB should have the same number of rows as A and the same number of columns as B. In this case, AB is a 1x4 matrix:

### Example Question #3 : Matrix Vector Product

Calculate , given

,

Explanation:

By definition,

.

### Example Question #6 : Matrix Vector Product

Calculate , given

Explanation:

By definition,

.  A matrix with only one entry is simply a scalar.

### Example Question #7 : Matrix Vector Product

Calculate , given

.

Can not be determined,  is not a vector.

Explanation:

By definition,

.

Explanation:

Explanation: