Let v1, V2 and v3 be three linearly independent vectors in R3.(a) Find the rank of the matrix A = [(v1 – v2) (v2 – v3) (V3 – V1)].(b) Find the rank of the matrix B = [(v1 + v2) (V2 + V3) (V3 + V1)].

Let v1, v2 and v3 be linearly independent vectors. That is, αv1+βv2+γv3=0 ⇒ α=β=γ=0. (a) Let…

Let v1, V2 and v3 be three linearly independent vectors in R³. (a) Find the rank of the matrix A = [(v1 – v2) (v2– V3) (v3 – V1)]. (b) Find the rank of the matrix B = [(v1 + v2) (V2+vV3) (V3+V1)]. %3D

Let v1, V2 and v3 be three linearly independent vectors in R³. (a) Find the rank of the matrix A = [(v1 – v2) (v2– V3) (v3 – V1)]. (b) Find the rank of the matrix B = [(v1 + v2) (V2+vV3) (V3+V1)]. %3D

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 56EQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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Let v1, V2 and v3 be three linearly independent vectors in R3.
(a) Find the rank of the matrix A = [(v1 – v2) (v2 – v3) (V3 – V1)].
(b) Find the rank of the matrix B = [(v1 + v2) (V2 + V3) (V3 + V1)].

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