Q2) LU Decomposition, Vector Spaces and LT [1 i Find the LU decomposition of the matrix A = 0 1] a a a when it exists. b b a For which real numbers a and b does it exist? ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1], [1, 2, 0, -4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space. (1) iii Suppose that A is a matrix such that the complete solution to 4 Ax = 1 is of the form : x=1+c2 ,CER 8+8 (a) What can be said about the columns of matrix A? (b) Find the dimension of null space and rank of matrix A.

Q2) LU Decomposition, Vector Spaces and LT [1 i Find the LU decomposition of the matrix A = 0 1] a a a when it exists. b b a For which real numbers a and b does it exist? ii Find the dimension of the vector space spanned by the vectors {[1, 1, -2,0, 1], [1, 2, 0, -4, 1], [0, 1, 3, -3, 2], [2, 3, 0, -2,0]} and find a basis for the space. (1) iii Suppose that A is a matrix such that the complete solution to 4 Ax = 1 is of the form : x=1+c2 ,CER 8+8 (a) What can be said about the columns of matrix A? (b) Find the dimension of null space and rank of matrix A.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...

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