True or false questions . (Provide short explanation ) (a) If A is an 2 × 2 matrix with positive entries, than det A > 0. (b) If A and B are 2×2 matrices such that det A = 1 and det B = −2, then det (3(BA)^tr) = −18. (Here, G^tr indicates the transpose of G.) (c) If A is a 3 × 3 matrix such that det A = 7, then det(A^−1) = −7
True or false questions . (Provide short explanation ) (a) If A is an 2 × 2 matrix with positive entries, than det A > 0. (b) If A and B are 2×2 matrices such that det A = 1 and det B = −2, then det (3(BA)^tr) = −18. (Here, G^tr indicates the transpose of G.) (c) If A is a 3 × 3 matrix such that det A = 7, then det(A^−1) = −7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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True or false questions . (Provide short explanation )
(a) If A is an 2 × 2 matrix with positive entries, than det A > 0.
(b) If A and B are 2×2 matrices such that det A = 1 and det B = −2,
then det (3(BA)^tr) = −18.
(Here, G^tr indicates the transpose of G.)
(c) If A is a 3 × 3 matrix such that det A = 7, then det(A^−1) = −7.
(d) If A and B are 3 × 3 matrices, then det(A + B) = det A + det B.
(e) If A is a diagonal 3 × 3 matrix with numbers d1 = 4 and d2 = −3 and d3 = 4 positioned along the main diagonal, then det A = −48.
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