Prove the theorem (AB)^T = B^TA^T.
Complete the first step of the proof by filling in t...
Mathematics, 19.02.2020 23:12 claythememe
Prove the theorem (AB)^T = B^TA^T.
Complete the first step of the proof by filling in the blank.
The (i, j)-entry of (AB)^T is the (j, i)-entry of AB, which is a_j1 b_1i +... + a_jn b_ni.
Complete the second step of the proof by filling in the blank.
The entries in row i of B^T are b _1i, b_ni.
Complete the third step of the proof by filling in the blank.
The entries in column j of A^T are a_j1, a_jn.
Complete the fourth step of the proof by filling in the blank.
The (i, j)-entry in B^TA^T is a_j1 b_1i +... + a_jn b_ni.
Write a conclusion by filling in the blank.
Therefore. (AB)^T = B^TA^T.
Answers: 2
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