Problems on Matrices

In the problems on matrices article, we will look at the concepts of Matrices with the help of matrix questions and solutions and matrix word problems and solutions. The problems on matrices will cover many different properties of matrices like equity of matrices, matrix multiplication, matrix addition, etc.

One should know that addition and subtraction of two or more matrices can only be done if the numbers of rows and columns are equal in both the matrices, i.e., for two matrices X = [xij]mxn and Y = [yij]pxq, mxn = pxq (i.e., m=p and n=q).

With our help, you would no longer need to solve matrix equation calculators. So, let’s get started! 

Equity of Matrices 

Matrices A = [aij] and B = [bij] are considered equal if they are of the same order or aij = bij, for all i and j. 

Matrices questions and solutions 1- Find the values of a, b, c, x, y, and z. 

If  [x+5  z+9   2y-7] = [   6   11   3y-2]and [ a+2    2c-2      b-6]= [-3   0     2b+4]     

We all know that if two matrices are equal, their corresponding elements are also equal. 

Therefore, 

x+5 = 6                      z+9 = 11                  2y-7 = 3y-2

a+2 = -3                     2c-2 = 0                   b – 6 = 2b + 4

After simplifying, we get the following values: 

a = -5, b = 10, c = 1, x = 1, z = 2, and y = -5 

Addition of Matrices 

Matrices word problem and solutions 1- Zubin has two factories A and B. Each factory produces school bags for boys and girls in three different colours – blue, red and yellow. The quantities produced by each factory is represented in the matrices below.

Let boys and girls be represented as columns 1 and 2, respectively, and the colours blue, red and yellow can be represented as rows 1, 2 and 3, respectively.

From this, we can conclude that the total bags produced in each colour for boys and girls are 

Blue: Boys = 170, Girls = 110

Red: Boys = 145, Girls = 120

Yellow: Boys = 165, Girls = 160.

Multiplication of a matrix by a scalar

Matrices questions and solutions 2- For two matrices X and Y, when is XY defined?

Ans: For any two given matrices X and Y, the scalar product XY is defined only if the number of columns in matrix X equals the number of rows in matrix Y, i.e., XY is defined for two matrices when

X = [xij]mxn and Y = [yij]pxq , n = p.

Matrices questions and solutions 3- Find matrix X, if 2A + 3X = 5B and A =

Solving for X,

2A + 3X = 5B 

• 3X = 5B – 2A 

• X = 13 (5B -2A) 

• X = 1/3

Conclusion 

With this, we conclude our article on problems on matrices. We hope that our article was insightful and that matrices word problems and solutions helped clear your doubts. The concept of matrices is used in several fields of mathematics and physics because matrices make it easier to calculate complex equations. This concept is applied in the study of quantum mechanics, optics, invertibility, etc.