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 ______.

विकल्प

• k = 3, p = n

• k is arbitrary, p = 2

• p is arbitrary, k = 3

• k = 2, p = 3

Answer 1

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