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HW11P2: Linear Dependence/Independence (10 points) \begin{bmatrix} 5\\\ 0\\\ 0\\\ -1 \end{bmatrix}, V? = \begin{bmatrix} 6\\\ -1\\\ 0\\\ 0 \end{bmatrix}, V? = \begin{bmatrix} 6\\\ -4\\\ 2\\\ 0 \end{bmatrix}, V? = \begin{bmatrix} 8\\\ 1\\\ 6\\\ -12 \end{bmatrix} a) Represent each vector as a column in a matrix and find its rank. i. State whether the vectors are linearly dependent or linearly independent and why, and identify their span. ii. Given ANY b vector, what type of system can be created with these vectors and how many solutions can be found? b) Evaluate the determinant of the matrix of vectors in (a). Hint, use your solution of part (a) to evaluate the determinant using the determinant properties i. State whether the vectors are linearly dependent or linearly independent and why.

          HW11P2: Linear Dependence/Independence (10 points)
\begin{bmatrix} 5\\\ 0\\\ 0\\\ -1 \end{bmatrix}, V? = \begin{bmatrix} 6\\\ -1\\\ 0\\\ 0 \end{bmatrix}, V? = \begin{bmatrix} 6\\\ -4\\\ 2\\\ 0 \end{bmatrix}, V? = \begin{bmatrix} 8\\\ 1\\\ 6\\\ -12 \end{bmatrix}
a) Represent each vector as a column in a matrix and find its rank.
i. State whether the vectors are linearly dependent or linearly independent and
why, and identify their span.
ii. Given ANY b vector, what type of system can be created with these vectors and
how many solutions can be found?
b) Evaluate the determinant of the matrix of vectors in (a). Hint, use your solution of
part (a) to evaluate the determinant using the determinant properties
i. State whether the vectors are linearly dependent or linearly independent and
why.

HW11P2: Linear Dependence/Independence (10 points)

< b m a t r i x >
, V? =
< b m a t r i x >
, V? =
< b m a t r i x >
, V? =
< b m a t r i x >

a) Represent each vector as a column in a matrix and find its rank.
i. State whether the vectors are linearly dependent or linearly independent and
why, and identify their span.
ii. Given ANY b vector, what type of system can be created with these vectors and
how many solutions can be found?
b) Evaluate the determinant of the matrix of vectors in (a). Hint, use your solution of
part (a) to evaluate the determinant using the determinant properties
i. State whether the vectors are linearly dependent or linearly independent and
why.

Added by Inmaculada S.

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