Solve the problem.
-$$A = \left[ \begin{array} { r r r r r }
1 & 3 & - 4 & 0 & 1 \
2 & 4 & - 5 & 2 & - 4 \
1 & - 5 & 0 & - 3 & 2 \
- 3 & - 1 & 8 & 3 & - 4
\end{array} \right] , B = \left[ \begin{array} { r r r r r }
1 & 3 & - 4 & 0 & 1 \
0 & - 2 & 3 & 2 & - 6 \
0 & 0 & - 8 & - 11 & 25 \
0 & 0 & 0 & 0 & 0
\end{array} \right]$$
A) $\{ ( 1,3 , - 4,0,1 ) , ( 2,4 , - 5,2 ) , - 4 , ( 1 , - 5,0 , - 3,2 ) , ( - 3 , - 1,8,3 , - 4 ) \}$

B) $\{ ( 1,0,0,0 ) , ( 3 , - 2,0,0 ) , ( - 4,3 , - 8,0 ) \}$

C) $\{ ( 1,3 , - 4,0,1 ) , ( 0 , - 2,3,2 , - 6 ) , ( 0,0 , - 8 , - 11,25 ) , ( 0,0,0,0,0 ) \}$

D) $\{ ( 1,3 , - 4,0,1 ) , ( 0 , - 2,3,2 , - 6 ) , ( 0,0 , - 8 , - 11,25 ) \}$

Question

Solve the problem.
-$$A = \left[ \begin{array} { r r r r r } 
1 & 3 & - 4 & 0 & 1 \
2 & 4 & - 5 & 2 & - 4 \
1 & - 5 & 0 & - 3 & 2 \
- 3 & - 1 & 8 & 3 & - 4
\end{array} \right] , B = \left[ \begin{array} { r r r r r } 
1 & 3 & - 4 & 0 & 1 \
0 & - 2 & 3 & 2 & - 6 \
0 & 0 & - 8 & - 11 & 25 \
0 & 0 & 0 & 0 & 0
\end{array} \right]$$
A) $\{ ( 1,3 , - 4,0,1 ) , ( 2,4 , - 5,2 ) , - 4 , ( 1 , - 5,0 , - 3,2 ) , ( - 3 , - 1,8,3 , - 4 ) \}$

B) $\{ ( 1,0,0,0 ) , ( 3 , - 2,0,0 ) , ( - 4,3 , - 8,0 ) \}$

C) $\{ ( 1,3 , - 4,0,1 ) , ( 0 , - 2,3,2 , - 6 ) , ( 0,0 , - 8 , - 11,25 ) , ( 0,0,0,0,0 ) \}$

D) $\{ ( 1,3 , - 4,0,1 ) , ( 0 , - 2,3,2 , - 6 ) , ( 0,0 , - 8 , - 11,25 ) \}$

Quizplus · Accepted Answer

Matrix B is in row echelon form and represents the row space of matrix A. The correct choice, C, lists all the non-zero rows of matrix B, which are the basis vectors for the row space of A.

Solve the Problem A) {(1,3,−4,0,1),(2,4,−5,2),−4,(1,−5,0,−3,2),(−3,−1,8,3,−4)}\{ ( 1,3 , - 4,0,1 ) , ( 2,4 , - 5,2 ) , - 4 , ( 1 , - 5,0 , - 3,2 ) , ( - 3 , - 1,8,3 , - 4 ) \}{(1,3,−4,0,1),(2,4,−5,2),−4,(1,−5,0,−3,2),(−3,−1,8,3,−4)}

Solve the Problem A) $\{ ( 1,3 , - 4,0,1 ) , ( 2,4 , - 5,2 ) , - 4 , ( 1 , - 5,0 , - 3,2 ) , ( - 3 , - 1,8,3 , - 4 ) \}$