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  • Assume X, Y, Z, W and P are matrices of order 2 by n, 3 by k, 2 by p, n by 3 and p by k, respectively. Choose the correct answer in Exercises 21 and 22. The restriction on n, k and p so that PY + WY will be defined are: (A) k equals 3 (B) k is arbitrary

Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. Choose the correct answer in Exercises 21 and 22.

    Q21.    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

Answers (1)

best_answer

P and Y are of order p*k  and 3*k respectively.

\therefore  PY will be defined only if k=3, i.e. order of PY is p*k.

W and Y are of order n*3  and 3*k respectively.

\therefore  WY is  defined because the number of columns of W is equal to the number of rows of Y which is 3, i.e. the order of WY is n*k

Matrices PY and WY can only be added if they both have same order i.e =  n*k  implies p=n.

Thus, k = 3, p = nare restrictions on n, k and p so that PY + WY will be defined.

Option (A) is correct.

Posted by

seema garhwal

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