### All Precalculus Resources

## Example Questions

### Example Question #7 : Multiplication Of Matrices

Compute:

**Possible Answers:**

**Correct answer:**

A scalar that multiplies a one by two matrix will result in a one by two matrix.

Multiply the scalar value with each value in the matrix.

### Example Question #1 : Matrices

Evaluate:

**Possible Answers:**

**Correct answer:**

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

### Example Question #1 : Matrices

Simplify:

**Possible Answers:**

**Correct answer:**

Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.

### Example Question #1 : Matrices

What is ?

**Possible Answers:**

**Correct answer:**

You can begin by treating this equation just like it was:

That is, you can divide both sides by :

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore,

### Example Question #41 : Matrices And Vectors

Find 3A given:

**Possible Answers:**

Not possible

**Correct answer:**

To multiply a scalar and a matrix, simly multiply each number in the matrix by the scalar. Thus,

### Example Question #1 : How To Find Scalar Interactions With A Matrix

If , what is ?

**Possible Answers:**

**Correct answer:**

Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :

Now, this means that your equation looks like:

This simply means:

and

or

Therefore,

### Example Question #1 : Find The Product Of Two Matrices

Find .

**Possible Answers:**

No Solution

**Correct answer:**

The dimensions of A and B are as follows: A= 3x3, B= 3x1

When we mulitply two matrices, we need to keep in mind their dimensions (in this case 3x* 3 and 3*x1).

**The two inner numbers need to be the same.** Otherwise, we cannot multiply them. The product's dimensions will be the two outer numbers: 3x1.

### Example Question #2 : Find The Product Of Two Matrices

Find .

**Possible Answers:**

No Solution

**Correct answer:**

The dimensions of both A and B are 2x2. Therefore, the matrix that results from their product will have the same dimensions.

Thus plugging in our values for this particular problem we get the following:

### Example Question #41 : Matrices And Vectors

Find .

**Possible Answers:**

No Solution

**Correct answer:**

The dimensions of A and B are as follows: A=1x**3**, B= **3**x1.

Because the two inner numbers are the same, we **can** find the product.

The two outer numbers will tell us the dimensions of the product: 1x1.

Therefore, plugging in our values for this problem we get the following:

### Example Question #1 : Find The Product Of Two Matrices

Find .

**Possible Answers:**

No Solution

**Correct answer:**

No Solution

The dimensions of A and B are as follows: A= 3x**1**, B= **2**x3

In order to be able to multiply matrices, the inner numbers need to be the same. In this case, they are 1 and 2. As such, we **cannot** find their product.

The answer is **No Solution**.