1.

Find x, y, a and b if \(\begin{bmatrix} 2x -3y & a - b & 3 \\[0.3em] 1 & x + 4y & 3a + 4b \\[0.3em] \end{bmatrix}\) = \(\begin{bmatrix} 1& -2 &3 \\[0.3em] 1 & 6 & 29 \\[0.3em] \end{bmatrix}\)

Answer»

Given

\(\begin{bmatrix} 2x -3y & a - b & 3 \\[0.3em] 1 & x + 4y & 3a + 4b \\[0.3em] \end{bmatrix}\)= \(\begin{bmatrix} 1& -2 &3 \\[0.3em] 1 & 6 & 29 \\[0.3em] \end{bmatrix}\)

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

Given as two matrices are equal.

So by equating them

2a + b = 4 …… (1)

And a – 2b = – 3 …… (2)

And 5c – d = 11 …… (3)

4c + 3d = 24 …… (4)

On multiplying equation (1) by 2 and adding to equation (2)

4a + 2b + a – 2b = 8 – 3

⇒ 5a = 5

⇒ a = 1

Substitute this value of a in equation (1)

2 × 1 + b = 4

⇒ 2 + b = 4

⇒ b = 4 – 2

⇒ b = 2

On multiplying equation (3) by 3 and adding to equation (4)

15c – 3d + 4c + 3d = 33 + 24

⇒ 19c = 57

⇒ c = 3

Substitute this value of c in equation (4)

4 × 3 + 3d = 24

⇒ 12 + 3d = 24

⇒ 3d = 24 – 12

⇒ 3d = 12

⇒ d = 4

So a = 1, b = 2, c = 3 and d = 4


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