6. Determine whether the following statements are true or false and providea justification for your response.а.If the columns of a matrix A form a basis for R", then A is invertible.125b. There must be 125 vectors in a basis for R'c. If B = {v1, V2, ..., Vn} is a basis of R", then every vector in R" can beexpressed as a linear combination of basis vectors.d. The coordinates {x}, are the weights that form x as a linearcombination of basis vectors.If the basis vectors form the columns of the matrix Cg, then{x}s°е.Cgx.

Answered: Image /qna-images/answer/500f39ea-9ba0-48d0-bb90-13511ca91809.jpg

6. Determine whether the following statements are true or false and provide a justification for your response. а. If the columns of a matrix A form a basis for R", then A is invertible. b. There must be 125 vectors in a basis for R25. If B = {v1, v2, ..., Vn} is a basis of R", then every vector in R" can be expressed as a linear combination of basis vectors. С.

6. Determine whether the following statements are true or false and provide a justification for your response. а. If the columns of a matrix A form a basis for R", then A is invertible. b. There must be 125 vectors in a basis for R25. If B = {v1, v2, ..., Vn} is a basis of R", then every vector in R" can be expressed as a linear combination of basis vectors. С.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.1: Orthogonality In Rn

Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...

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