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(15+15+10) A 3 × 3 matrix M has columns V₁, V2, V3 (in that order). (a) (₁) Compute the determinant of the matrix whose columns are 30₁, 302, 303, in that order. (b) () Compute the determinant of the matrix whose columns are 57₁−102, 5√2+V3, 503, in that order. (c) Compute the determinant of the matrix whose rows are 501 - 102, 502 + V3, 503, in that order.

(15+15+10) A 3 × 3 matrix M has columns V₁, V2, V3 (in that order). (a) (₁) Compute the determinant of the matrix whose columns are 30₁, 302, 303, in that order. (b) () Compute the determinant of the matrix whose columns are 57₁−102, 5√2+V3, 503, in that order. (c) Compute the determinant of the matrix whose rows are 501 - 102, 502 + V3, 503, in that order.

Advanced Engineering Mathematics
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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### Problem Statement Given a \(3 \times 3\) matrix \(M\) with columns \(\vec{v}_1, \vec{v}_2, \vec{v}_3\) (in that order): #### Tasks (a) \(\left(\frac{-1}{15}\right)\) Compute the determinant of the matrix whose columns are \(3\vec{v}_1, 3\vec{v}_2, 3\vec{v}_3\), in that order. (b) \(\left(\frac{-1}{15}\right)\) Compute the determinant of the matrix whose columns are \(5\vec{v}_1 - 1\vec{v}_2, 5\vec{v}_2 + \vec{v}_3, 5\vec{v}_3\), in that order. (c) \(\left(\frac{-1}{10}\right)\) Compute the determinant of the matrix whose rows are \(5\vec{v}_1 - 1\vec{v}_2, 5\vec{v}_2 + \vec{v}_3, 5\vec{v}_3\), in that order.
Transcribed Image Text:### Problem Statement Given a \(3 \times 3\) matrix \(M\) with columns \(\vec{v}_1, \vec{v}_2, \vec{v}_3\) (in that order): #### Tasks (a) \(\left(\frac{-1}{15}\right)\) Compute the determinant of the matrix whose columns are \(3\vec{v}_1, 3\vec{v}_2, 3\vec{v}_3\), in that order. (b) \(\left(\frac{-1}{15}\right)\) Compute the determinant of the matrix whose columns are \(5\vec{v}_1 - 1\vec{v}_2, 5\vec{v}_2 + \vec{v}_3, 5\vec{v}_3\), in that order. (c) \(\left(\frac{-1}{10}\right)\) Compute the determinant of the matrix whose rows are \(5\vec{v}_1 - 1\vec{v}_2, 5\vec{v}_2 + \vec{v}_3, 5\vec{v}_3\), in that order.
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