Difference between revisions of "031 Review Part 2, Problem 11"

Revision as of 19:18, 9 October 2017

Consider the following system of equations.

x_{1}+kx_{2}=1

3x_{1}+5x_{2}=2k

Find all real values of $k$ such that the system has only one solution.

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">Consider the following system of equations.
-    \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>x_1+kx_2=1</math>
-    \begin{bmatrix}
-& 0 & -1 & 5 \\
-& -2  & 5 & -6 \\
-& 0 & 0 & 0
-         \end{bmatrix}.</math>
-<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>
+::<math>3x_1+5x_2=2k</math>
+<span class="exam">Find all real values of &nbsp;<math style="vertical-align: 0px">k</math>&nbsp; such that the system has only one solution.