Question

Problem 6 to 9 refer to the matrices A and B below. Make appropriate calculations that justify your answers and mention an appropriate theorem. \begin{bmatrix} 1 & 3 & 0 & 3 \\ -1 & -1 & -1 & 1 \\ 0 & -4 & 2 & -8 \\ 2 & 0 & 3 & -1 \end{bmatrix} A = \begin{bmatrix} 1 & 3 & -2 & 2 \\ 0 & 1 & 1 & -5 \\ 1 & 2 & -3 & 7 \\ -2 & -8 & 2 & -1 \end{bmatrix} B = 6. How many rows of A contain a pivot position? Does the equation Ax=b have a solution for each b in R?? 7. Do the columns of B span R?? Does the equation Bx=y have a solution for each y in R?? 8. Can each vector in R? be written as a linear combination of the columns of the matrix A above? Do the columns of A span R?? 9. Can every vector in R? be written as a linear combination of the columns of the matrix B above? Do the columns of B span R??

          Problem 6 to 9 refer to the matrices A and B below. Make appropriate calculations that justify your
answers and mention an appropriate theorem.
\begin{bmatrix} 1 & 3 & 0 & 3 \\ -1 & -1 & -1 & 1 \\ 0 & -4 & 2 & -8 \\ 2 & 0 & 3 & -1 \end{bmatrix} A = \begin{bmatrix} 1 & 3 & -2 & 2 \\ 0 & 1 & 1 & -5 \\ 1 & 2 & -3 & 7 \\ -2 & -8 & 2 & -1 \end{bmatrix} B =
6. How many rows of A contain a pivot position? Does the equation Ax=b have a solution for each b in
R??
7. Do the columns of B span R?? Does the equation Bx=y have a solution for each y in R??
8. Can each vector in R? be written as a linear combination of the columns of the matrix A above? Do the
columns of A span R??
9. Can every vector in R? be written as a linear combination of the columns of the matrix B above? Do the
columns of B span R??

Problem 6 to 9 refer to the matrices A and B below. Make appropriate calculations that justify your
answers and mention an appropriate theorem.

< b m a t r i x >
A =
< b m a t r i x >
B =
6. How many rows of A contain a pivot position? Does the equation Ax=b have a solution for each b in
R??
7. Do the columns of B span R?? Does the equation Bx=y have a solution for each y in R??
8. Can each vector in R? be written as a linear combination of the columns of the matrix A above? Do the
columns of A span R??
9. Can every vector in R? be written as a linear combination of the columns of the matrix B above? Do the
columns of B span R??

Added by Lindsey A.

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