how to solve matrix

Tutorial on How to solve Matrix with Examples

Students are always scared of Mathematics although maths is very easy if you understand the rationale and logics of mathematical concepts instead of mugging up each and every question of maths. Students frequently ask how to solve n numbers of concepts and matrix is one of them. Matrix is basically the representation of numbers or linear equations in block format in order to solve them. You can also add or subtract or multiply two or matrices with each other. This is why many students struggle with matrices and ask how to solve them. This article will teach you the method of solving the matrix in an easy step by step manner with examples.

Steps – How to solve Matrix

1.  First step to solve the matrix is to check if you have the sufficient data to find out the each variable of the linear equation by using a matrix.

Matrix is used to solve the linear equation but there should be more than one linear equation in order to use the matrix method. Thus if you have two equations only then also you can use the matrix method to find out the variables.

Assignment help

Each linear equation has certain variables which we need to find out and such variables have certain coefficients. Let’s understand it through given example –

2x + 3y – 5z = 2

Here, x, y and z are variables of the equation which we need to find out and +2, +3 and -5 are the coefficients in the equation.

2. Second step in How to solve the Matrix is to write down your equations in standard form. Next question is what is the standard form of writing a linear equation then the answer is Ax + By + Cz = D.

So you have to write all the equations in such form in order to find out the values of variables using matrix.

It is not necessary that you have only 3 variables; there can be less than 3 variables and similarly there can be more than 3 variables. If you have more than 3 variables then you will add them in the left side after the z variable for example – Ax + By + Cz + Dw = E.

Here, A, B, C and D are coefficients and x, y, z, we are the variables.

3. Next step in How to solve Matrix is to transfer the data of the equation in matrix form. So the next thing to learn is how to write down equations in matrix form. Lets understand it through examples suppose we have following 3 equations –

x + 2y – 3z = 5

x + y + z = 6

2x + y – z = 1

Now we need to find out the variables using matrix format.  As we can see the equations are already in standard form so we can proceed with transferring such equations into matrix form.

We write down the coefficients of each equation in row form one after another. So here we will first write down the  1, 2 and -3 in the first row of the matrix thereafter we will write the coefficients of the second equation and then the 3rd equation. Look at below to understand better –

Here, the rows and columns are also named. So we can name Row 1 as R1 which has 1, 2 and -3, Row 2 as R2 which has 1, 1 and 1 and similarly row 3 as R3 which has 2, 1 and -1.

Likewise we can also name columns as C1, C2 and C3. C1 has 1, 1 and 2, C2 has 2, 1 and 1 and lastly C3 has -3, 1 and -1.

4. Next step in how to solve the matrix is to put large brackets around the first and last column to make it a matrix. Thus you will put square brackets [] around the whole block. It is just a symbol of matrices and nothing else you don’t have to worry or scare about the same.

5. Next thing to learn in solving matrices is to add two matrices. You can add or subtract the two matrices.

Suppose the two matrices are

And second is

You can now add the matrices by adding R1 with the R1 of the second matrix and similarly all the numbers of the block.

Thus, you will get

Similarly you will perform other functions like subtraction or multiplication etc.


We all get scared even with the name of mathematics. We find difficulty in solving most of the concepts and we panic with the name of mathematics but the fact is if we understand the logic of solving the mathematical problems then we can easily solve all the problems irrespective of the complexity. Many students face problems in solving matrices. They also follow the steps and guides on how to solve matrices in an easy way. Get the best help with math homework from the experts.

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