Difference between revisions of "031 Review Part 2, Problem 2"

Revision as of 19:07, 9 October 2017

Find the dimension of the subspace spanned by the given vectors. Are these vectors linearly independent?

{\begin{bmatrix}1\\0\\2\end{bmatrix}},{\begin{bmatrix}3\\1\\1\end{bmatrix}},{\begin{bmatrix}-2\\-1\\1\end{bmatrix}},{\begin{bmatrix}5\\2\\2\end{bmatrix}}

Foundations:

Solution:

Step 1:

Step 2:

Final Answer:

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the matrix &nbsp;<math style="vertical-align: -31px">A=
+<span class="exam"> Find the dimension of the subspace spanned by the given vectors. Are these vectors linearly independent?
-    \begin{bmatrix}
-& -4 & 9 & -7 \\
-           -1 & 2  & -4 & 1 \\
-& -6 & 10 & 7
-         \end{bmatrix}</math>&nbsp; and assume that it is row equivalent to the matrix
-::<math>B=
+::<math>\begin{bmatrix}
-    \begin{bmatrix}
+\\
-& 0 & -1 & 5 \\
+\\
-& -2  & 5 & -6 \\
-& 0 & 0 & 0
+          \end{bmatrix},
-          \end{bmatrix}.</math>
+         \begin{bmatrix}
+  \\
-<span class="exam">(a) List rank &nbsp;<math style="vertical-align: 0px">A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">\text{dim Nul }A.</math>
+\\
-<span class="exam">(b) Find bases for &nbsp;<math style="vertical-align: 0px">\text{Col }A</math>&nbsp; and &nbsp;<math style="vertical-align: 0px">\text{Nul }A.</math>&nbsp; Find an example of a nonzero vector that belongs to &nbsp;<math style="vertical-align: -5px">\text{Col }A,</math>&nbsp; as well as an example of a nonzero vector that belongs to &nbsp;<math style="vertical-align: 0px">\text{Nul }A.</math>
+         \end{bmatrix},
+         \begin{bmatrix}
+           -2  \\
+           -1 \\
+         \end{bmatrix},
+         \begin{bmatrix}
+  \\
+\\
+         \end{bmatrix}</math>