Given 3[(x, y), (z, w)] = [(x, 6), (-1, 2w)] + [(4, x + y), (z + w, 3)

1.	Given 3[(x, y), (z, w)] = [(x, 6), (-1, 2w)] + [(4, x + y), (z + w, 3)], find the values of x, y, z and w.
Answer» By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get 3x = x + 4⇒ 2x = 4 ⇒ x = 2 and 3y = 6 + x + y ⇒ 2y = 6 + x ⇒ y = (6 + x)/2 Putting the value of x, we get y = (6 + 2)/2 = 8/2 = 4 Now, 3z = −1 + z + w, 2z = −1 + w z = (-1 + w)/2 .....(ii) Now, 3w = 2w + 3 ⇒ w = 3 Putting the value of w in Eq. (i), we get z = (-1 + 3)/2 = 2/2 = 1 Hence, the values of x, y, z and w are 2, 4, 1 and 3.

Given 3[(x, y), (z, w)] = [(x, 6), (-1, 2w)] + [(4, x + y), (z + w, 3)], find the values of x, y, z and w.

Answer»

By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get

3x = x + 4⇒ 2x = 4 ⇒ x = 2

and 3y = 6 + x + y ⇒ 2y = 6 + x

⇒ y = (6 + x)/2

Putting the value of x, we get

y = (6 + 2)/2 = 8/2 = 4

Now, 3z = −1 + z + w, 2z = −1 + w

z = (-1 + w)/2 .....(ii)

Now, 3w = 2w + 3 ⇒ w = 3

Putting the value of w in Eq. (i), we get

z = (-1 + 3)/2 = 2/2 = 1

Hence, the values of x, y, z and w are 2, 4, 1 and 3.

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Given 3[(x, y), (z, w)] = [(x, 6), (-1, 2w)] + [(4, x + y), (z + w, 3)], find the values of x, y, z and w.

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