Monday, June 18, 2018

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

Tuesday, June 5, 2018

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

Tuesday, April 24, 2018

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

In a previous blog post, we talked about one type of multiplication for matrices, scalar multiplication. In this blog post be will talk about the other type of multiplication for matrices, matrix multiplication.

Matrix multiplication is when you multiply matrix A, an n x m matrix, by matrix B, an m x p matrix, to get their product, matrix C, and n x p matrix. This means you can only multiply matrices, where matrix A has the same amount of columns as there are rows in matrix B.

In order to multiply matrices, we will have to calculate the dot product of the rows of the first matrix, matrix A, and the columns of the second matrix, matrix B.

Let’s see what this looks like:


 



In words, what we are seeing is the dot product of the first row of matrix A and the first column of matrix B make an element in the 1st row and 1st column of their product. The dot product of the second row of matrix A and the first column of matrix B make an element in the 2nd row and 1st column. The dot product of the first row of matrix A and the second column of matrix B make an element in the 1st row and 2nd column. And so on . . .

Now, let’s see some examples to help better understand how multiply matrices.

First example (click here):


1. Take the dot product of the rows of matrix A and the columns of matrix B


2. Simplify


Next example (click here):


1. Take the dot product of the rows of matrix A and the columns of matrix B


2. Simplify


Last example (click here):


1. Take the dot product of the rows of matrix A and the columns of matrix B


2. Simplify


Matrix multiplication can be difficult and tricky, when learning it for the first time. The more you practice it, the more it’ll become second nature to you. Check out Symbolab’s Practice for practice problems and quizzes on this topic.

Until next time,

Leah

Saturday, March 31, 2018

High School Math Solutions - Matrix Transpose Calculator, Transpose

The transpose of a matrix is when you turn all the rows of a matrix into columns and vice versa. Row 1 becomes column 1, row 2 becomes column 2, and so on. The transpose of a matrix, A, is denoted A^T.

When you transpose a matrix, the element in row i, column j becomes the element in row j, column i of the transposed matrix.

Let’s see some examples to better understand what the transpose of a matrix is.

First example (click here):


1. Turn the rows into columns


Next example (click here):


1. Turn the rows into columns


Last example (click here):


1. Turn the rows into columns


This concept can be hard to visualize, so practicing a few examples will help you understand and become familiar with the transpose of a matrix. For more help or practice on the transpose of a matrix and other related matrix topics, visit Symbolab’s Practice.

Until next time,

Leah

Wednesday, March 21, 2018

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