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In Exercises 24–26, use determinants to decide if the set of vectors is linearly independent.$$\left[\begin{array}{r}{7} \\ {-4} \\ {-6}\end{array}\right],\left[\begin{array}{r}{-8} \\ {5} \\ {7}\end{array}\right],\left[\begin{array}{r}{7} \\ {0} \\ {-5}\end{array}\right]$$

independent

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

01:33

In Exercises 24–26, use de…

01:50

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In Exercises $5-8,$ determ…

03:56

03:31

In Exercises $1-4,$ determ…

03:06

02:43

03:48

02:21

Determine by inspection wh…

were given a set of vectors and were asked He's determinants to decide if this set of vectors is linearly. Independent vectors are seven negative. Four negative six negative 857 and 70 Negative five. Well, to determine if these vectors are linearly independent, consider The Matrix seven. With columns seven Negative four Negative six eight Negative 857 and 70 Negative five. So this is the Matrix whose columns are these vectors and let's evaluate the determinant. So there are few from ways to do this. Um, I think the simplest way here is just going to be a straight up expansion. So expanding across the third column, we have our co factors seven times. Determinant of the Matrix and negative four five negative 67 plus co. Factor negative five times the determinant of the matrix. Seven. Negative eight Negative four five In evaluating. This gives us seven times this is negative. 28 plus 30 is too plus negative five times and then we have 35 minus 32 is three so 14, minus 15 or negative one. And this is, of course, non zero. And since the determinant of this matrix is non zero. And this is a matrix whose column vectors are vectors. Well, the columns of our matrix form a linearly independent set and therefore are vectors are linearly independent.

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