Use determinants to decide if the set of vectors is

actever6a

actever6a

Answered question

2021-12-01

Use determinants to decide if the set of vectors is linearly independent.
[462],[707],[352]

Answer & Explanation

Antum1978

Antum1978

Beginner2021-12-02Added 15 answers

The columns of the matrix form a linearly independent set if and only if determinant of matrix is non-zero.
Start by cofactor expansion along first column and then use formula for determinant of 2×2 matrix:
|473605272|=4|0572|6|7372|+2|7305|
=4(0*(-2)-7*(-5))-6(-7*(-2)-7*(-3))
=2(-7*(-5)-0*(-3))
=4*35-6*35+2*35=0
Result:
Since determinant is zero, the columns form a linearly dependent set.

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