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Mathematics · JEE | MATRICES
हिन्दीIf \( X, Y, Z, W, \) and \( P \) are matrices of order \( 2 \times n, 3 \times k, 2 \times p, n \times 3, \) and \( p \times k \) respectively, what is the restriction on \( n, k, \) and \( p \) so that \( PY + WY \) is well-defined?
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Correct answer · Option C
\( k = 3, p = n \)
Explanation
For \( PY \) to be defined, columns of \( P \) (\( k \)) must equal rows of \( Y \) (\( 3 \)), so \( k = 3 \). For \( WY \) to be defined, columns of \( W \) (\( 3 \)) must equal rows of \( Y \) (\( 3 \)). For addition \( PY + WY \), their orders must be equal, hence rows of \( P \) must equal rows of \( W \), i.e., \( p = n \).
