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(b) Let aji aj2 _a]3 A= |a21 a22 a23 |аз1 аз2 аз3 2a11 2a12 2a13 and B = a11+a21 a12+a22 a13 +a23 a32 азз If det(A) = Esgn(o)a16(1)a20(2)a30(3), determine det(B) in terms of det(A). If det(A) = 6, compute det(B). (i) (ii) %3D

(b) Let aji aj2 _a]3 A= |a21 a22 a23 |аз1 аз2 аз3 2a11 2a12 2a13 and B = a11+a21 a12+a22 a13 +a23 a32 азз If det(A) = Esgn(o)a16(1)a20(2)a30(3), determine det(B) in terms of det(A). If det(A) = 6, compute det(B). (i) (ii) %3D

Linear Algebra: A Modern Introduction
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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(а) Let u, v and w be vectors in R³. The volume(u, v, w) is given by determinant of [u v w). (i) Derive the volume(4u +v,u+ 2w, – 3v+w) in terms of volume(u, v, w). (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) Let aj a12 a13 2a13 2a12 2a11 and B= |a|1+a2ı _aj2+a22 a13+a23 A = a21 a22 аз1 аҙ2 а33 a23 a31 a32 аз (i) If det(A) = Esgn(o)a1o(1)a2o(2)az0(3), determine det(B) in terms of det(A). (ii) If det(A) = 6, compute det(B).
Transcribed Image Text:(а) Let u, v and w be vectors in R³. The volume(u, v, w) is given by determinant of [u v w). (i) Derive the volume(4u +v,u+ 2w, – 3v+w) in terms of volume(u, v, w). (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) Let aj a12 a13 2a13 2a12 2a11 and B= |a|1+a2ı _aj2+a22 a13+a23 A = a21 a22 аз1 аҙ2 а33 a23 a31 a32 аз (i) If det(A) = Esgn(o)a1o(1)a2o(2)az0(3), determine det(B) in terms of det(A). (ii) If det(A) = 6, compute det(B).
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