An unknown 3 x 3 matrix A using rowoperations eor_1, ero_2, ero_3 and ero_4. In this order, the matrix can be formed into an identity matrix eroj: -3rı +r2 → r2 ero2: -3r3 → r3 ero3: rį + r2 ero4: 5r3 +r| → r| a) For every i = 1, 2, 3, 4 the elementary matrix Eirthat is the same as ero_i. Argue for one of the following matrix products. AE,E3E2E1, AE,E2E3E4, E¡E2E3E4A eller E4E3E2E¡A must be the identity matrix. Which one is it? List another one of these four products which provides the identity matrix. b) For each i = 1, 2, 3, 4 in the elementary matrix E, 'and apply these to dedice A. c) Let X be row 2 and 3 in the matrix EE,E,E, and set 3 -5 0 -43] B Show that X is the inverse to B Decide all left inverse to B Does matrix B have any right inverse?
An unknown 3 x 3 matrix A using rowoperations eor_1, ero_2, ero_3 and ero_4. In this order, the matrix can be formed into an identity matrix eroj: -3rı +r2 → r2 ero2: -3r3 → r3 ero3: rį + r2 ero4: 5r3 +r| → r| a) For every i = 1, 2, 3, 4 the elementary matrix Eirthat is the same as ero_i. Argue for one of the following matrix products. AE,E3E2E1, AE,E2E3E4, E¡E2E3E4A eller E4E3E2E¡A must be the identity matrix. Which one is it? List another one of these four products which provides the identity matrix. b) For each i = 1, 2, 3, 4 in the elementary matrix E, 'and apply these to dedice A. c) Let X be row 2 and 3 in the matrix EE,E,E, and set 3 -5 0 -43] B Show that X is the inverse to B Decide all left inverse to B Does matrix B have any right inverse?
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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Transcribed Image Text:An unknown 3 x 3 matrix A using rowoperations eor_1, ero_2, ero_3 and ero_4. In this order, the matrix
can be formed into an identity matrix
eroj: –3rı +r2 → r2
ero2: -3r3 → r3
ero3: rį + r2
ero4: 5r3 +r| → ri
a) For every i = 1, 2, 3, 4 the elementary matrix Pirthat is the same as ero_i. Argue for one of the
following matrix products.
AE,E3E2E1, AE1E2E3E4, E¡E2E3E4A eller E4E3E2E1A
must be the identity matrix. Which one is it? List another one of these four products
which provides the identity matrix.
b) For each i = 1, 2, 3, 4 in the elementary matrix E, 'and apply these to dedice A.
c) Let X be row 2 and 3 in the matrix E,E,E,E, and set
B = 3
0 -43
-5
Show that X is the inverse to B
Decide all left inverse to B
Does matrix B have any right inverse?
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