USING OPERATIONS ON MATRICES FINDING UNKNOWNS

Solve each equation or state if there is no unique solution.

Problem 1 :

Solution:

25 - 3x = 15

-3x = 15 - 25

-3x = -10

x = 10/3

Problem 2 :

Solution :

The order of matrices on both sides are equal. By equating the corresponding terms, we get

-3x = 9 + y

-3x - y = 9 -----(1)

y + 5 = x

-x + y = -5 -----(2)

(1) + (2)

-3x + (-x) = 9 + (-5)

-4x = 4

x = -1

Applying the value of x in (1), we get

-3(-1) - y = 9

3 - y = 9

y = 9 - 3

y = 6

Problem 3 :

Solution :

3x + y = 13 -------(1)

4x - 2y = 24

Dividing by 2, we get

2x - y = 12 -----(2)

(1) + (2)

3x + y + 2x - y = 13 + 12

5x = 25

x = 5

applying the value of x in (2)

2(5) - y = 12

10 - y = 12

y = 10 - 12

y = -2

Problem 4 :

Solution :

Problem 5 :

Solution :

By equating the corresponding terms,