Question

@Moderators
@BrainlyStars
@Best Users


Assume X, Y, Z, W and P are matrices of order 2 x 11, 3.x k, 2 x p. 1x3 ad px respectively. Choose the correct answer in Exercises 21 and 22

21. The restriction on n, k and p so that PY + WY will be defined are: (A) k = 3, p=n (B) k is arbitrary, p = 2 (C) p is arbitrary, k = 3 (D) k = 2, p = 3

22. If n = p, then the order of the matrix 7X - 5Z is: (A) p × 2 (B) 2 × n (C) n × 3 (D) p ×


Please don't spam!!! ​

Answer 1

Appropriate Question :-

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 x p, n × 3 and p × k respectively.

Choose the correct answer in Exercises 21 and 22

21. The restriction on n, k and p so that PY + WY will be defined are:

(A) k = 3, p=n

(B) k is arbitrary, p = 2

(C) p is arbitrary, k = 3

(D) k = 2, p = 3

22. If n = p, then the order of the matrix 7X - 5Z is:

(A) p × 2

(B) 2 × n

(C) n × 3

(D) p × n

$\large\underline{\sf{Solution-}}$

Given that

The order of the matrices are as follow

• X has 2 × n

• Y has 3 × k

• Z has 2 x p

• W has n × 3

and

• P has p × k

Solution :- 21

So, PY is defined and resultant matrix has the order p × 3.

Now, WY is defined and resultant matrix has order n × k.

Now, we know that,

Addition of matrix is defined when both the matrices have same order.

So, PY + WY is defined when p = n and k = 3.

So, option A is correct.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Solution :- 22

Now, matrix X has the order 2 × n

And matrix Z has the order 2 × p

Further, given that p = n.

Order of 7X - 5Z is 2 × n or 2 × p

So, option B is correct.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More to Learn

Matrix multiplication is defined when number of columns of pre multiplier is equal to number of rows of post multiplier.

• Matrix multiplication may or may not be Commutative.

• Matrix multiplication is Associative.

• Matrix multiplication is Distributive.

Answer 2

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

$\large\sf\fbox\pink{Appropriate Question :-}$

Assume X, Y, Z, W and P are matrices of order 3 x 11, 3.x k, 2 x p. 1x3 ad px respectively.

The restriction on n, k and p so that PY + WY will be defined are: (A) k = 3, p=n (B) k is arbitrary, p = 2 (C) p is arbitrary, k = 3 (D) k = 2, p = 3

$\large\sf\fbox\pink{Solution :-}$

Y, Z, W, P are of type 3 x k, 2 x p, n x 3, p x k respectively.

Since PY is defined

.•. number of columns of P = number of rows of Y

.•. k = 3

Now PY is of type p x k and WY is of type n x k

Scince PY + WY is defined

.•. P = n

.•. ( A ) is correct answer.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

⇝ sorry if there any mistake in my answer

BeBrainly :-)