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

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

High School Math Solutions - Matrix Add, Subtract Calculator, Matrices

A matrix is an array of numbers, symbols, or expressions that are displayed in rows and columns. The dimension of a matrix are written as r x n, where r is the number of rows and n is the number of columns. One thing you can do with matrices is add or subtract them together. The only caveat to adding or subtracting matrices is that the matrices must be the same size, i.e. must have the same dimension.

Adding and subtracting matrices is simple. Simply, add or subtract each element in the matching position, creating a new matrix with the same dimension. Let’s visualize this to get a better understanding.

Here is how to add matrices together:

You’d follow the same method for subtraction.

Here is an example of matrices that can’t be added together because they aren’t the same size:

You can see one matrix is 2x2 and the other is 2x3.

Let’s see some examples to better understand.

Here’s the first example (click here):

1. Add elements in the matching positions

2. Simplify

Next example (click here):

1. Add elements in the matching positions

2. Simplify

Last example (click here):

1. Add elements in the matching positions

2. Simplify

As you can see, adding and subtracting matrices is pretty simple. If you are interested in practicing more problems on this topic or want more help on this topic, check out Symbolab’s Practice.

Until next time,

Leah