Question

20. Use Gaussian elimination to solve the following vector equation for its unique solution. Then, illustrate that solution as both (1) an intersection of two lines in a plane and (2) weights in a linear combination of vectors. $x_1 \begin{bmatrix} -1 \\ 1 \end{bmatrix} + x_2 \begin{bmatrix} 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 4 \end{bmatrix}$

          20. Use Gaussian elimination to solve the following vector equation for its unique solution.
Then, illustrate that solution as both (1) an intersection of two lines in a plane and (2) weights
in a linear combination of vectors.
$x_1 \begin{bmatrix} -1 \\ 1 \end{bmatrix} + x_2 \begin{bmatrix} 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 2 \\ 4 \end{bmatrix}$

20. Use Gaussian elimination to solve the following vector equation for its unique solution.
Then, illustrate that solution as both (1) an intersection of two lines in a plane and (2) weights
in a linear combination of vectors.
x1
< b m a t r i x >
+ x2
< b m a t r i x >
=
< b m a t r i x >

Added by Phillip P.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Joy Squicciarini

Step 1

The given vector equation is x1[1, 2] + x2[3, 4] = [3]. We can rewrite this equation as a matrix equation: [1, 3] * [x1, x2] = [3]. Show more…

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20. Use Gaussian elimination to solve the following vector equation for its unique solution. In a linear combination of vectors, then illustrate that solution as both (1) an intersection of two lines in a plane and (2) weights x[] + x2[1] = [3].