Two matrices are equal if and only if the matrices have the same shape and elements in corresponding positions are equal.
Example 1 :
If
find p, q, r and s.
Solution :
Both are 2x 2 matrices, so they are equal and their corresponding terms will be equal.
By equating corresponding terms, we get
p = 9 |
q+1 = -2 q = -2-1 q = -3 |
r2 = 4 r = √4 r = ±2 |
5 = s s = 5 |
So, the values of p, q, r and s are 9, -3, ±2 and 5 respectively.
Example 2 :
Solution :
By equating corresponding terms, we get
a = 1, b = -5, c = 2 and d = 3.
Example 3 :
Solution :
By equating corresponding terms, we get
x = -2
a = 5
2a = b
By applying the value of a in 2a = b, we get
2(5) = b
b = 10
So, the value of x is -2, a = 5 and b = 10.
Example 4 :
Solution :
By equating corresponding terms, we get
x = 4
1-y = 0
y = 1
z = -2
So, the value of x is 4, y = 1 and z = -2.
Example 5 :
Solution :
x2 = 9
x = ±3
But equating x-1 to 2, we get
x = 3
y = -y y+y = 0 2y = 0 y = 0 |
z = z2 z2 - z = 0 z(z-1) = 0 z = 0 and z = 1 |
So, the value of x is 3, y = 0 and z = 0 or 1.
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