How To Multiply a Matrix By 2 | Scalar Matrix Multiplication

How to multiply a matrix by a scalar

Do you know how to multiply a matrix by 2? Well, multiplying a matrix with number such as two is very easy. This kind of multiplication is called scalar multiplication. You can multiply any matrix of any order or dimension with any number whether it is whole number or real number, positive or negative.

To multiply a matrix by 2 there are three steps. First set the problem accordingly. Second multiply the given number with each entry in the matrix. Third write the result in the corresponding columns and rows.

We are going to learn how to multiply a matrix by 2.Look at (2) the number out of matrix or near the matrix or out of the bracket. This is the number we are going to multiply with numbers inside the matrix. We will multiply 2 with each number in matrix.

Keep in mind that there are three rows and two columns in the given matrix. So they will remain same when we get the answer. You can not get more rows and columns than the given number of columns and rows.

How to solve the problem?

We have to multiply the matrix A by 2 as given above.
Let’s solve the problem.

Step 1. Take 2 and multiply each number in the matrix with it.

Step 2. Now solve each multiplication.

That’s it. We have solved the matrix multiplication by 2.

How to multiply a matrix by a constant?

In matrices any real number you multiply with a matrix is called scalar value. So you can also say it a constant. It is very simple and easy to multiply a matrix by a constant. All you need is how to multiply two numbers, I am sure that you have already learnt multiplication of numbers.

Multiply a matrix by a constant is same as multiplying a matrix by 2. We have already solved this above. All the steps are same and simple.

Let’s take an example here. If

Then find 3B.

Solution of the problem:

you can say the given problem is how to multiply a matrix by 3. Here the constant number is 3. So we are going to multiply it with each element in the matrix B. You must observe the number of rows and columns.

Step 1. Set the problem.

Step 2.  Multiply 3 with each entry in the matrix.

Step 3.  Write the result of multiplication.

Now, I think, you have got it. If you have not don’t worry. We will solve further problems. Observe them and follow the steps.

How to multiply a matrix by a scalar?

Solving scalar multiplication is also same as multiplying a matrix by a constant. So it is going to be very easy to solve it.

Multiplying a matrix by a scalar value is not tough. All you have to do is set the given problem accordingly, multiply each digit in the matrix with the given scalar value, and write the result of product.

Before going further let’s learn definition of  Scalar multiplication.

What is scalar matrix multiplication?

Definition: Scalar matrix multiplication is defined as the product of a matrix with a scalar.( Source)

The term scalar multiplication states that it is the product of a real number and a matrix. (Source)
So you can say multiplication of a matrix by a real number is called scalar matrix multiplication.

Now take one more example.

If

Then find 5C.

Solving scalar matrix multiplication:

Here in this problem the scalar value is 5. To solve the problem we follow the steps below.

Step 1.

Step 2. 

Step 3. 

This is the answer. I hope you have understood all.If you are facing problem in calculation, you can use matrix multiplication calculator apps. I have written detailed post on ten best matrix multiplication calculator apps.

We have covered multiplication of a matrix by a real number, and a constant. in addition to this we also multiplied a matrix by a scalar, and learnt definition of scalar multiplication. 

I would love to answer your queries. Comment below if you have any question related to the topic.