# EQUALITY OF MATRICES

Two matrices can be equal, if they have the same order and corresponding elements are equal.

Example :

The above two matrices have the same order 3x2. That is, 3 rows and 2 columns.

Further,

 a = uc = we = y b = vd = xf = z

## Solved Problems

Problem 1 :

Find the values of w, x, y and z from the following equation.

Solution :

Since the given two matrices are equal, the corresponding elements must be equal.

Then, we have

 w = 1y = 0 x = -3z = 7

Problem 2 :

Find the values of w, x, y and z from the following equation.

Solution :

 2p = 10 ----(1)3t = 9 ----(2) 5p + q = 17 ----(3)5t + r = 15 ----(4)

Solve (1) for p.

2p = 10

p = 5

Substitute p = 5 into (3).

5(5) + q =17

25 + q = 17

q = -8

Solve (2) for t.

3t = 9

t = 3

Substitute r = 5 into (3).

5(3) + r =15

15 + r = 15

r = 0

Therefore,

p = 5, q = -8, t = 3, r = 0

Problems 3-5 : Find the values of x, y and z from the following equations.

Problem 3 :

Solution :

(x, y, z) = (3, 12, 3)

Problem 4 :

Solution :

x + y = 6 ----(1)

5 + z = 5 ----(2)

xy = 8 ----(3)

Solve (1) for y.

y = 6 - x ----(4)

Substitute y = 6 - x into (3).

x(6 - x) = 8

6x - x2 = 8

x- 6x +  8 = 0

x- 2x - 4x + 8 = 0

x(x - 2) - 4(x - 2) = 0

(x - 2)(x - 4) = 0

x - 2 = 0  or  x - 4 = 0

x = 2  or  x  = 4

Substitute x = 2 and 4 into (4).

 y = 6 - 2y = 4 y = 6 - 4y = 2

Solve (2) for z.

5 + z = 5

z = 0

Therefore,

(x, y, z) = (2, 4, 0)  or  (4, 2, 0)

Problem 5 :

Solution :

x + y + z = 9 ----(1)

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

y + z = 7 ----(3)

Substitute y + z = 7 into (1)

x + 7 = 9

x = 2

Substitute x = 2 into (2).

2 + z = 5

z = 3

Substitute z = 3 into (3).

y + 3 = 7

y = 4

Therefore,

(x, y, z) = (2, 4, 3)

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