Question

4. Let $A = \begin{bmatrix} 3 & 2 & 10 & -6 \\ 1 & 0 & 2 & -4 \\ 0 & 1 & 2 & 3 \\ 1 & 4 & 10 & 8 \end{bmatrix}$ and $b = \begin{bmatrix} -1 \\ 3 \\ -1 \\ 4 \end{bmatrix}$. (a) Find all x in $\mathbb{R}^4$ that are mapped into the zero vector by the transformation $x \mapsto Ax$. (b) Is b in the range of the linear transformation $x \mapsto Ax$? Why or why not?

          4. Let $A = \begin{bmatrix} 3 & 2 & 10 & -6 \\ 1 & 0 & 2 & -4 \\ 0 & 1 & 2 & 3 \\ 1 & 4 & 10 & 8 \end{bmatrix}$ and $b = \begin{bmatrix} -1 \\ 3 \\ -1 \\ 4 \end{bmatrix}$.
(a) Find all x in $\mathbb{R}^4$ that are mapped into the zero vector by the transformation $x \mapsto Ax$.
(b) Is b in the range of the linear transformation $x \mapsto Ax$? Why or why not?

4. Let A =
< b m a t r i x > and b =
< b m a t r i x >.
(a) Find all x in ℝ^4 that are mapped into the zero vector by the transformation x ↦ Ax.
(b) Is b in the range of the linear transformation x ↦ Ax? Why or why not?

Added by Mark L.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Madhur L

12/23/2022

Step 1

Step 1: To find all x in R^4 that are mapped into the zero vector by the transformation x -> Ax, we need to solve the equation Ax = 0. Show more…

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Let A=[[3,2,10,-6],[1,0,2,-4],[0,1,2,3],[1,4,10,8]] and b=[[-1],[3],[-1],[4]] (a) Find all x in R^(4) that are mapped into the zero vector by the transformation x|->Ax. (b) Is b in the range of the linear transformation x|->Ax ? Why or why not? 2 10 9- 1 0 2 -4 0 1 2 8 1 4 10 8 3 1 4.LetA= andb= 4 (a) Find all x in R4 that are mapped into the zero vector by the transformation x Ax (b) Is b in the range of the linear transformation x Ax? Why or why not?