Matrices Addition

In mathematics, a matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers, such as

[[1, 9, 13], [20, 55, 4]]

An item in a matrix is called an entry or an element. The example has entries 1, 9, 13, 20, 55, and 4. Entries are often denoted by a variable with two subscripts, as shown on the right. Matrices of the same size can be added and subtracted entry wise and matrices of compatible sizes can be multiplied. (Source: Wikipedia)

This article explains you about add two matrices, some solved problems on add two matrices and practice problems on adding two matrices.

Solved Problems on addition of matrices

Method to add matrices:

We can add the matrix with same order only.

By adding corresponding elements of two matrices we can get the sum of two matrix.

Problem 1:

Add the following two matrices

A = [[2,-5],[9,7]] B = [[9,6],[-4,0]]

Solution:

Given, Two matrix A = [[2,-5],[9,7]] ,  B = [[9,6],[-4,0]]

We need to find the addition .

That is A + B

A + B =  [[2,-5],[9,7]]  + [[9,6],[-4,0]]

We know that, By adding corresponding elements of two matrices we can get the sum of two matrix.

A + B =  [[2+9,-5+6],[9+(-4),7+0]]

= [[11,1],[5,7]]

Answer: A + B = [[11,1],[5,7]]

Problem 2:

Add the following two matrices,

P = [[23, 54, -31],[12, -72, 41]] and Q = [[ -9, 8, 0],[31,38,-45]]

Solution:

Given, Two matrix P = [[23, 54, -31],[12, -72, 41]] and Q = [[ -9, 8, 0],[31,38,-45]]

We need to add the above two matrix.

Both are 2 by 3 matrix. By adding corresponding elements of two matrices we can get the sum of two matrix.

P + Q =  [[23, 54, -31],[12, -72, 41]] + [[ -9, 8, 0],[31,38,-45]]

= [[23+ (-9), 54+8, -31+0],[12+31, -72+38, 41+(-45)]]

= [[14, 62, -31],[43, -34, -4]]

Answer: P + Q = [[14, 62, -31],[43, -34, -4]]

Problem 3:

Find the value of x, if  A = [[2,3x], [5,6]] , B = [[6,-3],[8,-2]] and A+B = [[8,12],[13,4]]

Solution:

Given, A = [[2,3x], [5,6]] , B = [[6,-3],[8,-2]] and A+B = [[8,12],[13,4]]

We need to find the x value.

A + B = [[8,12],[13,4]]

[[2,3x], [5,6]] + [[6,-3],[8,-2]] =  [[8,12],[13,4]]

[[2+6,3x-3],[5+8,6-2]] = [[8,12],[13,4]]

[[8, 3x-3],[13,4]] =  [[8,12],[13,4]]

In this corresponding elements are equal.

So we can take, 3x-3 = 12

Add 3 on both sides,

3x-3 + 3 = 12 + 3

3x = 15

Divide by 3 on both sides,

x = 5

Answer: The value of x = 5

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Practice problems on addition of matrices

Problems:

1. Add two matrices P = [[ -2,-4],[4,9]] and Q = [[8, 5],[2,-7]]

2. Find the value of  x , if  X = [[0,-2],[3,6]] , Y = [[ 2,-5],[x,4]] and X + Y = [[ 2,-7],[ 8, 10]]

Solution:

1. P + Q = [[6,1],[6,2]]

2. x = 5