Same chapter3 marksDifficulty: Medium
Define a symmetric and a skew-symmetric matrix, and state what can be said about the diagonal of a skew-symmetric matrix.
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3 marksDifficulty: Medium
Prove that (AB)T = BTAT for matrices for which the product is defined.
Original Khojo Papers practice question — not from a past board paper.
Answer
The element in row i and column j of (AB)T is the element in row j and column i of AB, which is the sum over k of a(j,k)b(k,i). The element in row i and column j of BTAT is the sum over k of b(k,i)a(j,k), which is the same. So the two matrices are equal.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
The order of the factors must be reversed, which is easy to forget.
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