(a) Check whether the vector (3,-1, 4) can be expressed as a linear combination of u = (1,-1,0), v = (0,1,1) and w = (3,-5,-2).(b) Determine which subsets below are subspaces of given V.1) V = R, W = {(x,y, z) | a+2y-3z = 4}2) V = Mn (R), W= subset of non-singular matrices

We need to check whether the vector can be expressed as linear combination or not. NOTE - As per our…

Answered: (a) Check whether the vector (3,-1, 4)…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 42EQ

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(a) Check whether the vector (3,-1, 4) can be expressed as a linear combination of u = (1, -1,0), v = (0,1,1) and w = (3,-5,-2) (b) Determine which subsets below are subspaces of given V. 1) V = R, W = {(x, y, z) | x+ 2y 3z = 4} 2) V = M, (R), W= subset of non-singular matrices