Difference between revisions of "031 Review Part 2, Problem 8"

Revision as of 19:16, 9 October 2017

Let $A={\begin{bmatrix}1&3&8\\2&4&11\\1&2&5\end{bmatrix}}.$ Find $A^{-1}$ if possible.

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Solution:

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Final Answer:

@@ Line 1: / Line 1: @@
-<span class="exam">Consider the matrix &nbsp;<math style="vertical-align: -31px">A=
-    \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=
+<span class="exam">Let &nbsp;<math style="vertical-align: -31px">A=
      \begin{bmatrix}
-& 0 & -1 & 5 \\
+& 3 & 8 \\
-& -2  & 5 & -6 \\
+& 4 &11\\
-& 0 & 0 & 0
+& 2 & 5
-          \end{bmatrix}.</math>
+          \end{bmatrix}.</math>&nbsp; Find &nbsp;<math style="vertical-align: 0px">A^{-1}</math>&nbsp; if possible.
-<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>