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Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det A" = det A c. JAC|= |A||C| d. Using property c above, show that det Ak = (det A)k for some natural number k. Show that detrA = r² det A, for some scalar r. е.

Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det A" = det A c. JAC|= |A||C| d. Using property c above, show that det Ak = (det A)k for some natural number k. Show that detrA = r² det A, for some scalar r. е.

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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Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det A" = det A c. |AC| = |A||C| d. Using property c above, show that det Ak = (det A)k for some natural number k. Show that detrA = r² det A, for some scalar r. е.
Transcribed Image Text:Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: a. If you exchange two rows of A to produce matrix B, then det(A) = -det(B). b. det A" = det A c. |AC| = |A||C| d. Using property c above, show that det Ak = (det A)k for some natural number k. Show that detrA = r² det A, for some scalar r. е.
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