1.

If \(\begin{bmatrix}x+3 & z+4 & 2y-7 \\[0.3em]4x+6 & a-1 & 0 \\[0.3em]b-3 & 3b &z+2c\end{bmatrix}​​\)= \(\begin{bmatrix}0 & 6 & 3y-2 \\[0.3em]2x & -3 & 2c+2 \\[0.3em]2b+4 & -21 &0\end{bmatrix}​​\)Obtain the values of a, b, c, x, y and z.

Answer»

Given two matrices are equal.

 \(\begin{bmatrix}x+3 & z+4 & 2y-7 \\[0.3em]4x+6 & a-1 & 0 \\[0.3em]b-3 & 3b &z+2c\end{bmatrix}​​\)= \(\begin{bmatrix}0 & 6 & 3y-2 \\[0.3em]2x & -3 & 2c+2 \\[0.3em]2b+4 & -21 &0\end{bmatrix}​​\)

We know that if two matrices are equal then the elements of each matrices are also equal.

∴x + 3 = 0 

⇒ x = 0 – 3 = – 3 …(1) 

And z + 4 = 6 

⇒ z = 6 – 4 = 2 …(2) 

And 2y – 7 = 3y – 2 

⇒ 2y – 3y = – 2 + 7 

⇒ – y = 5 ⇒ y = – 5 …(3) 

4x + 6 = 2x …(4) 

a – 1 = – 3 

⇒ a = – 3 + 1 = – 2 …(5)

2c + 2 = 0 

⇒ 2c = – 2 

⇒ c = – 1 … (6) 

b – 3 = 2b + 4

⇒ b – 2b = 4 + 3

⇒ – b = 7

⇒ b = – 7 … (7)

∴ x = – 3, 

y = – 5, 

z = 2 

and a = – 2, 

b = – 7, 

c = – 1


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