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1 -1 3 -2 1 1 -1 0 a | A = 2 reduced row-echelon form -2 2 -1 R=0 0 1 1 b %3D %3D -1 1 5 -4 0 0 0 C Find: (i) (ii) (iii) the values of a, b and c. a basis for the row space of A. a basis for the column space of A.

1 -1 3 -2 1 1 -1 0 a | A = 2 reduced row-echelon form -2 2 -1 R=0 0 1 1 b %3D %3D -1 1 5 -4 0 0 0 C Find: (i) (ii) (iii) the values of a, b and c. a basis for the row space of A. a basis for the column space of A.

Elementary Linear Algebra (MindTap Course List)
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 67E
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(а) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: 1. 1 -1 3 -2 1 -1 0 a A = 2 -2 2 -1 reduced row-echelon form R=0 0 1 b %3D -1 15-4 0 0 0 C Find: (i) (ii) (iii) (iv) (v) (vi) the values of a, b and c. a basis for the row space of A. a basis for the column space of A. a basis for the null space of A. rank (A). nullity (A"). (b) If the column vectors in the matrix A are denoted as v,, v,, V3, V4, express each vector that is not in the basis, as a linear combination of the basis vectors.
Transcribed Image Text:(а) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: 1. 1 -1 3 -2 1 -1 0 a A = 2 -2 2 -1 reduced row-echelon form R=0 0 1 b %3D -1 15-4 0 0 0 C Find: (i) (ii) (iii) (iv) (v) (vi) the values of a, b and c. a basis for the row space of A. a basis for the column space of A. a basis for the null space of A. rank (A). nullity (A"). (b) If the column vectors in the matrix A are denoted as v,, v,, V3, V4, express each vector that is not in the basis, as a linear combination of the basis vectors.
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