Suppose V₁, V₂ € R³ are nonzero column vectors and V3 = 2v₁ - 3₂. What is the determinantof the matrix (V1 V2 V3)?

Given: Suppose are nonzero column vectors and We have to find what is the determinant of the…

Answered: Suppose V₁, V₂ € R³ are nonzero column…

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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Question

Suppose V₁, V₂ € R³ are nonzero column vectors and V3 = 2v₁ - 3₂. What is the determinant
of the matrix (V1 V2 V3)?

Expert Solution

Step 1: Solution

Given: Suppose $stack v subscript 1 with rightwards arrow on top comma space stack v subscript 2 with rightwards arrow on top space element of straight real numbers cubed$ are nonzero column vectors and $stack v subscript 3 with rightwards arrow on top equals 2 stack v subscript 1 with rightwards arrow on top minus 3 stack v subscript 2 with rightwards arrow on top.$

We have to find what is the determinant of the matrix $open parentheses table row cell stack v subscript 1 with rightwards arrow on top end cell cell stack v subscript 2 with rightwards arrow on top end cell cell stack v subscript 3 with rightwards arrow on top end cell end table close parentheses space ?$