Question

Determine if w is in​ Col(A). Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The vector w is not in​ Col(A) because Axequalsw is an inconsistent system. One row of the reduced row echelon form of the augmented matrix​ [A 0] has the form​ [0 0​ b] where bequals nothing. B. The vector w is not in​ Col(A) because w is a linear combination of the columns of A. C. The vector w is in​ Col(A) because Axequalsw is a consistent system. One solution is xequals nothing. D. The vector w is in​ Col(A) because the columns of A span set of real numbers R squared.

Answer 1

Answer:

option c

The vector w is in Col(A) because Ax = w is a consistent system. One solution is x = 0 or 1/2

Step-by-step explanation:

$A = \left[\begin{array}{cc}-4&8\\-2&4\end{array}\right] , w = \left[\begin{array}{c}2&1\end{array}\right]$

$null A = \left[\begin{array}{c}x_2&x_1\end{array}\right]$

$\left[\begin{array}{cc}-4&8\\-2&4\end{array}\right]\left[\begin{array}{c}x_1\\x_2\end{array}\right]=\left[\begin{array}{c}0\\0\end{array}\right]$

=>

$-4x_1 + 8x_2 = 0\\-2x_1 +4x_2 = 0$

$=> x_1 = 2x_2$

check the attached file for complete solution