Given

Given that two matrices are equal.

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

Therefore by equating them we get,

3x + 4y = 2 …… (1)

x – 2y = 4 …… (2)

a + b = 5 …… (3)

2a – b = – 5 …… (4)

Multiplying equation (2) by 2 and adding to equation (1), we get

3x + 4y + 2x – 4y = 2 + 8

⇒ 5x = 10

⇒ x = 2

Now, substituting the value of x in equation (1)

3 × 2 + 4y = 2

⇒ 6 + 4y = 2

⇒ 4y = 2 – 6

⇒ 4y = – 4

⇒ y = – 1

Now by adding equation (3) and (4)

a + b + 2a – b = 5 + (– 5)

⇒ 3a = 5 – 5 = 0

⇒ a = 0

Now, again by substituting the value of a in equation (3), we get

0 + b = 5

⇒ b = 5

∴ a = 0, b = 5, x = 2 and y = – 1

Answered by Aaryan | 1 year agoConstruct a 4 × 3 matrix A = [a_{i j}] whose elements a_{i j} are given by a_{i j} = i

Construct a 4 × 3 matrix A = [ai j] whose elements ai j are given by \( a_{i j} = \dfrac{(i – j)}{(i + j)}\)

Construct a 4 × 3 matrix A = [a_{i j}] whose elements a_{i j} are given by a_{i j} = 2i + \( \dfrac{i}{j}\)