6. Write the vector equation \( a\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]+b\left[\begin{array}{c}2 \\ -1 \\ 1\end{array}\right]+c\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right]=\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right] \) as a system of linear equations and solve it.
Added by Pavan Vinubhai G.
Close
Step 1
From the first equation, we can express a in terms of b: a = 1 - 2b. Substitute a = 1 - 2b into the third equation: Show more…
Show all steps
Your feedback will help us improve your experience
Muhammed Shafi and 96 other Discrete Mathematics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Recommended Videos
Determine the solution set to the sys$\operatorname{tem} A \mathbf{x}=\mathbf{b}$ for the given coefficient matrix $A$ and right-hand side vector b. $$A=\left[\begin{array}{rrr} 1 & 0 & 5 \\ 3 & -2 & 11 \\ 2 & -2 & 6 \end{array}\right], \mathbf{b}=\left[\begin{array}{l} 0 \\ 2 \\ 2 \end{array}\right]$$
Matrices and Systems of Linear Equations
Gaussian Elimination
Find the vector form of the general solution of the linear system $A \mathbf{x}=\mathbf{b},$ and then use that result to find the vector form of the general solution of $A \mathbf{x}=\mathbf{0}$. (a) $x_{1}-3 x_{2}=1$ $2 x_{1}-6 x_{2}=2$ (b) $x_{1}+x_{2}+2 x_{3}=5$ $\begin{aligned} x_{1} &+x_{3}=-2 \\ 2 x_{1}+x_{2}+3 x_{3} &=3 \end{aligned}$
General Vector Spaces
Row Space, Column Space, and Null Space
Write the system of equations with the given coefficient matrix and right-hand side vector. $$A=\left[\begin{array}{rrrr}1 & -1 & 2 & 3 \\1 & 1 & -2 & 6 \\3 & 1 & 4 & 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{r}1 \\-1 \\2\end{array}\right].$$
Terminology for Systems of Linear Equations
Recommended Textbooks
Discrete Mathematics and its Applications
Higher Level Mathematics
Discrete Mathematics
Watch the video solution with this free unlock.
EMAIL
PASSWORD