Consider the elementary matrices below.For A =det (A)For B =det (B) =For C ==det (C)=1 0000 10 1 01 00 k01000089101001 k0 1Now if M is an arbitrary matrix with det (M) = 4, thendet (BM) =

Answered: Image /qna-images/answer/a2cab1e9-d25a-44f2-a854-a8bea6620a78.jpg

Answered: Consider the elementary matrices below.…

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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2. Consider the matrix A = [10 -3 0 1 00 3 (a) Find elementary matrices E₁ and E2 such that E2E₁A = I. (b) Write A-¹ as a product of two elementary matrices. (c) Write A as a product of two elementary matrices.
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If A = b c d I then A is invertible if ad-bc0, in which case A-1 = If ad bc = 0, then A is not invertible. Find the inverse of the given matrix (if it exists) using the theorem above. (If this is not possible, enter DNE in any single blank. Enter sqrt(n) for √n.) ↓ 1 1 ad - bc -C 5/√2 -5/√2 5/√2 5/√2 d -b |
Let M be a 3 x 3 invertible matrix. Q2.1 Then det (2M-1) = none of the above -2 det (M) 1 8 det(M) 8 det (M) 2 det(M) 1 det (M) Q2.2 Then det (21 M) = 2 + det(M) always. False True

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Consider the elementary matrices below. 1 For A = 0 0 det (A) = 1 0 0 For B = 0 k 0 0 0 1 det (B) = 1 For C = 0 0 0 0 0 1 1 0 det (C) = 0 0 1 k 01 Now if M is an arbitrary matrix with det (M) = 4, then det (BM) =