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Question
Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively.
The restrictions on n, k and p so that PY + WY will be defined are ______.
Options
k = 3, p = n
k is arbitrary, p = 2
p is arbitrary, k = 3
k = 2, p = 3
Solution
The restrictions on n, k and p so that PY + WY will be defined are k = 3, p = n.
Explanation:
Given matrices: X, Y, Z, W and P
Orders: 2 × n, 3 × k, 2 × p, n × 3, p × k
Order of P = p × k,
Order of Y = 3 × k
∴ PY is possible if k = 3
Order of PY = p × k = p × 3
Orders of W and Y are n × 3 and 3 × k = 3 × 3, respectively.
Order of WY = n × 3
The sum of PY and WY is possible only if both of them are of the same order.
p × 3 = n × 3 = p × n
∴ PY + WY is defined if p = n and k = 3
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