1b Question 1(а)Let u, v and w be vectors in R³. The volume(u, v, w) is given by determinant of[u v w).Derive the volume(4u+v, u +2w, –3v+ w) in terms of volume(u, v, w).(i)(ii)Hence, compute the volume(4u + v, u + 2w, –3v + w) when u = (2,1,1),v = (1,2,0) and w = (1,0, 1).(b)Let2a12and B = |a|+a2i _aj2+a22 a13+a23a|1 a12 aj32a|12a13A =a21 a22 a23a31 a32 A33A32a33If det(A) = Esgn(o)a,q(1)a20(2)a30(3), determine det(B) in terms of det(A).If det(A) = 6, compute det(B).(i)(ii)

The determinant is a scalar value that is a function of the entries of a square matrix. It allows…

Answered: (b) Let 2a13 2a12 a11+a21 a12+ a22…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 7AEXP

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(b) Let 2a13 2a12 a11+a21 a12+ a22 a13+a23 2a11 a11 a12 a13 A = a21 a22 a23 and B : a31 a32 a33 a32 A33 (i) If det(A) = £sgn(0)a1q(1)a2a(2)ªz0(3), determine det(B) in terms of det(A). %3D (ii) If det(A) = 6, compute det(B).