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Use determinants to decide if the set of vectors is linearly independent. ? -2 ? ? 1 ? ? -2 ? ? 6 ?, ? -5 ?, ? 0 ? ? -3 ? ? -2 ? ? 5 ? The determinant of the matrix whose columns are the given vectors is [ ]. (Simplify your answer.) Is the set of vectors linearly independent? A. The set of vectors is linearly independent, because the determinant is not zero. B. The set of vectors is linearly independent, because the determinant exists. C. The set of vectors is linearly dependent, because the determinant exists. D. The set of vectors is linearly dependent, because the determinant is not zero. 

          Use determinants to decide if the set of vectors is linearly independent.

? -2 ? ?  1 ? ? -2 ?
?  6 ?, ? -5 ?, ?  0 ?
? -3 ? ? -2 ? ?  5 ?

The determinant of the matrix whose columns are the given vectors is [ ].
(Simplify your answer.)

Is the set of vectors linearly independent?

A. The set of vectors is linearly independent, because the determinant is not zero.
B. The set of vectors is linearly independent, because the determinant exists.
C. The set of vectors is linearly dependent, because the determinant exists.
D. The set of vectors is linearly dependent, because the determinant is not zero.
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Use determinants to decide if the set of vectors is linearly independent. ? -2 ? ? 1 ? ? -2 ? ? 6 ?, ? -5 ?, ? 0 ? ? -3 ? ? -2 ? ? 5 ? The determinant of the matrix whose columns are the given vectors is [ ]. (Simplify your answer.) Is the set of vectors linearly independent? A. The set of vectors is linearly independent, because the determinant is not zero. B. The set of vectors is linearly independent, because the determinant exists. C. The set of vectors is linearly dependent, because the determinant exists. D. The set of vectors is linearly dependent, because the determinant is not zero.

Added by Tiffany B.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Use determinants to decide if the set of vectors is linearly independent. [ -2, 1, -2 ] [ 6, -5, 0 ] [ -3, -2, 5 ] The determinant of the matrix whose columns are the given vectors is . (Simplify your answer.) Is the set of vectors linearly independent? A. The set of vectors is linearly independent, because the determinant is not zero. B. The set of vectors is linearly independent, because the determinant exists. C. The set of vectors is linearly dependent, because the determinant exists. D. The set of vectors is linearly dependent, because the determinant is not zero.
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Transcript

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00:01 In this question, we are asked to determine linear independence of the given vectors using determinants.
00:07 And recall that vectors are linearly independent.
00:15 If and only if, the determinant is zero.
00:21 Determinant is non -zero.
00:26 So if the determinant is non -zero, then the vectors are linearly independent.
00:32 If it's zero, then they are linearly dependent.
00:36 And let's calculate the determinant.
00:46 What we are going to do is we will use co -factor expansion across down the last column.
01:01 We will cross out the last column and then we'll start crossing out the rows one by one.
01:08 We'll cross out the first row and then we need to write down negative 1 to the power of the sum of the indices of the position of the energy at the intersection.
01:25 So the coordinates of negative 2 in the matrix are the first row and sorry, yeah, third column, third column and the first row...
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