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Linear Algebra With Applications
Found in: Page 143
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

For which value(s) of the constant k do the vectors below form a basis of 4 ?

[1002] , [0103] ,[0014] , [234K]

The given vectors [1002] , [0103] ,[0014] , [234K]form a basis of 444 for all values of k-29 .

See the step by step solution

Step by Step Solution

Step 1: Definition of the basis

The vectorsv1,v2,...,vn in nn form a basis of nnnif (and only if) the matrix

A=v1....vn is invertible.

Step 2: Finding the determinant

Here we have



Step 3: Finding the values of k

Since it is given that the vectors [1002] , [0103] ,[0014] , [234K]form a basis of 4then the matrix A=[100201030014234k] must be invertible.


Since the matrix A is invertible, then the vectors [1002] , [0103] ,[0014] , [234K] form a basis of 44444 for all values of k-29 .

Step 4: Final Answer

The given vectors[1002] , [0103] ,[0014] , [234K] form a basis of 4for all values of k29

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