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1. (a) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: -1 3 -2 1 -1 0 a reduced row-echelon form R =0 0 1 A = 2 -2 2 -1 | %3D 1 1 5-4 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. a i)

1. (a) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: -1 3 -2 1 -1 0 a reduced row-echelon form R =0 0 1 A = 2 -2 2 -1 | %3D 1 1 5-4 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. a i)

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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1. (a) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: -1 3 -2 1 -1 0 a reduced row-echelon form R =0 0 1 A = 2 -2 2 -1 | %3D 1 1 5-4 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. a i)
Transcribed Image Text:1. (a) The reduced row-echelon form of the matrix A is shown to be matrix R, as given below: -1 3 -2 1 -1 0 a reduced row-echelon form R =0 0 1 A = 2 -2 2 -1 | %3D 1 1 5-4 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. a i)
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