Q1: Consider the following linear system, Solve by Gauss-Jordan elimination method (Reduced Echelon form). X1 + x2 - x3 - x4 = -1 2x1 +x2 + x3 + 2x4 = 1 Зх, — 2х2 + 2хз — 6х4 3—3 6x1 + x3 - 9x4 = -2 %3D Q2: Find all values of a for which following system have (i) No solution (ii) a unique solution (iii) Infinite many solution. x + y - z = 3 ; x + 2y + z = 3 ; x + y + (a? – 10)z = a Q3: Express A and A-1 as a product of elementary matrices. [1 0 51 A = 0 1 6 li o 31

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.2: Guassian Eliminationa And Guass-jordan Elimination
Problem 54E
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Q1: Consider the following linear system, Solve by Gauss-Jordan elimination method
(Reduced Echelon form).
X1 + x2 - x3 - x4 = -1
2x1 +x2 + x3 + 2x4 = 1
Зх, — 2х, + 2хз — 6х, 3—3
6x1 +x3 – 9x4 = -2
Q2: Find all values of a for which following system have (i) No solution (ii) a unique
solution (i) Infinite many solution.
x+y - z = 3 ; x+2y +z = 3 ; x+ y+ (a² – 10)z = a
Q3: Express A and A-1 as a product of elementary matrices.
[1 0 51
A = 0 1 6
li o 3.
Transcribed Image Text:Q1: Consider the following linear system, Solve by Gauss-Jordan elimination method (Reduced Echelon form). X1 + x2 - x3 - x4 = -1 2x1 +x2 + x3 + 2x4 = 1 Зх, — 2х, + 2хз — 6х, 3—3 6x1 +x3 – 9x4 = -2 Q2: Find all values of a for which following system have (i) No solution (ii) a unique solution (i) Infinite many solution. x+y - z = 3 ; x+2y +z = 3 ; x+ y+ (a² – 10)z = a Q3: Express A and A-1 as a product of elementary matrices. [1 0 51 A = 0 1 6 li o 3.
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