Question

2. Assume that \textit{A} is row equivalent to \textit{B}. $A = \begin{bmatrix} 1 & -3 & 4 & -1 & 9 \\ -2 & 6 & -6 & -1 & -10 \\ -3 & 9 & -6 & -6 & -3 \\ 3 & -9 & 4 & 9 & 0 \end{bmatrix}$ $B = \begin{bmatrix} 1 & -3 & 0 & 5 & -7 \\ 0 & 0 & 2 & -3 & 8 \\ 0 & 0 & 0 & 0 & 5 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$ a. Rank $A = \underline{3}$ dim Row $A = \underline{3}$ dim Nul $A = \underline{2}$ b. Find basis for Col $A$, Row $A$ and Nul $A.$

          2. Assume that \textit{A} is row equivalent to \textit{B}.

$A = \begin{bmatrix} 1 & -3 & 4 & -1 & 9 \\ -2 & 6 & -6 & -1 & -10 \\ -3 & 9 & -6 & -6 & -3 \\ 3 & -9 & 4 & 9 & 0 \end{bmatrix}$

$B = \begin{bmatrix} 1 & -3 & 0 & 5 & -7 \\ 0 & 0 & 2 & -3 & 8 \\ 0 & 0 & 0 & 0 & 5 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$

a. Rank $A = \underline{3}$
dim Row $A = \underline{3}$
dim Nul $A = \underline{2}$
b. Find basis for Col $A$, Row $A$ and Nul $A.$

2. Assume that A is row equivalent to B.

A =
< b m a t r i x >

B =
< b m a t r i x >

a. Rank A = 3
dim Row A = 3
dim Nul A = 2
b. Find basis for Col A, Row A and Nul A.

Added by Anthony M.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Zhumagali Shomanov

07/05/2022

Step 1

Given that A is row equivalent to B, we can find the rank and dimensions of A by analyzing the row-reduced form of B. For the first matrix A and B: A = [[1, -3, 4, -1, 9], [-2, 6, -6, -1, -10], [-3, 9, -6, -6, -3], [3, -9, 4, 9, 0]] B = [[1, -3, 0, 5, -7], [0, Show more…

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Assume that A is row equivalent to B. A=[[1,-3,4,-1,9],[-2,6,-6,-1,-10],[-3,9,-6,-6,-3],[3,-9,4,9,0]],B=[[1,-3,0,5,-7],[0,0,2,-3,8],[0,0,0,0, oot(5)(5)],[0,0,0,0,0]] a. RankA^()= dim Row A dimNu lA= b. Find basis for ColA,RowA and Nu lA. 2. Assume that A is row equivalent to B. 1 0 0 2 B= 0 0 0 0 0 0 0 0 -7 8 Dowe ) 10 A 3 3 -9 0 a.RankA= 3 dim Row A= 3 dim Nul A= 2 b.Find basis for Col A,Row A and Nul A.