High School Math Solutions - Matrix Multiply Calculator, Matrix Scalar Multiplication

Last blog post, we talked about how to add and subtract matrices. Now, we will start getting into multiplication for matrices. There are two types: scalar multiplication and matrix multiplication. In this blog post, we will talk about the simpler of the two, scalar multiplication.

Scalar multiplication is when you multiply a matrix by a value, called a scalar. In scalar multiplication, you multiply each element of the matrix by the scalar.

Here is what scalar multiplication looks like:

Pretty simple, right? Now, let’s see some examples.

First example (click here):

1. Multiply each of the matrix elements by the scalar

2. Simplify

Next example (click here):

1. Multiply each of the matrix elements by the scalar

2. Simplify

Last example (click here):

1. Multiply each of the matrix elements by the scalar

2. Simplify

As you can see, scalar multiplication is pretty simple. In a later blog post, we will go over matrix multiplication. For more help or practice on this topic, go to Symbolab’s Practice.

Until next time,

Leah

Advanced Math Solutions - Matrix Multiply, Power Calculator, Matrix Powers

If you haven’t mastered matrix multiplication, check out our last blog post on matrix multiplication before continuing onto the next topic. In this blog post, we will talk about powers of matrices.

The power, n, of a matrix, A, is when you multiply the matrix by itself n times. A matrix can only be raised to a power if it has the same number of rows and columns. Below you can visualize how to take the power of a matrix. (Note: The matrix is being multiplied by itself n times)

In order to take the power of a matrix:

1. Rewrite the problem (expand)
2. Multiply the first two matrices
3. Multiply the next matrix (if there is one) to the matrix produced in step 2
4. Multiply the next matrix (if there is one) to the matrix produced in step 3

And so on until you get your final matrix.

Let’s see some examples of how to take the power of a matrix to better understand..

First example (click here):

1. Rewrite the problem

2. Multiply the first two matrices

Next problem (click here):

 1.  Rewrite the problem

2. Multiply the first two matrices

3. Multiply the next matrix to the matrix produced in step 2

Last example (click here):

1. Rewrite the problem

2. Multiply the two matrices

As you can see, matrix powers aren’t complicated, as long as you’ve mastered your matrix multiplication. If you need more help with topic, check out Symbolab’s Practice, which will provide you with practice problems and quizzes.

Until next time,

Leah