PROBLEMS ON OPERATIONS ON MATRICES WITH UNKNOWN VALUES

Problem 1 :

Find x and y such that

Solution :

Equating corresponding terms.

2x - y = 1 --- (1)

x + y = 2 --- (2)

Adding (1) and (2) we get,

(2x - y) + (x + y) = 1 + 2

2x - y + x + y = 3

3x = 3

x = 3/3

x = 1

x = 1 substitute the equation (2).

1 + y = 2

y = 2 - 1

y = 1

So, the values of x and y is 1 and 1.

Problem 2 :

Solution :

The given two matrices are in the same order, so we may add these matrices. For that we have to combine the corresponding terms.

Problem 3 :

Solution :

Problem 4 :

Solve the matrix equation 5A + 3X = 2B for X,

Solution :

Given equation is 5A + 3X = 2B.

Problem 5 :

Determine whether the product matrix AB is defined. If defined, find the order of AB.

Solution :

Problem 6 :

Find the product AB.

Solution :

Problem 7 :

Find AB and BA, if possible.

Solution :

To find AB :

A is 2 × 2 matrix and B is 3 × 2 matrix.

Number of column in the first matrix and number of rows in the second matrix they are not same. So, product is defined.

To find BA :

B is 3 × 2 matrix and A is 2 × 2 matrix. The product of BA is defined.