Answer
a. Dimensions: 4 x 4
b. No
c. No
d. $x + 8y + 6z = -4$
$y - 3z = 5$
$2z = -7$
$x + y + z = 0$
Work Step by Step
These are the questions within each question that the book asks.
a. Dimension of matrix
b. Matrix in row-echelon form? Yes/No
c. Reduced row-echelon form? Yes/No
d. System of equations that the matrix represents
For a, the dimensions are indicated as rows * columns
For b. the matrix must have leading 1s that shift to the right in successive rows
For c, the matrix must have leading 1s that shift to the right in successive rows and to only have "0" above and below the leading 1s.
For d, substitute the matrix values into a system of equations.
Given $\left[\begin{array}{ll}
1 & 8 & 6 & -4\\
0 & 1 & -3 & 5\\
0 & 0 & 2 & -7\\
1 & 1 & 1 & 0
\end{array}\right]$
a. 4 rows, 4 columns. Dimensions: 4 x 4
b. Matrix is not row-echelon form; it does not have leading 1s that shift to the right in successive rows
c. The matrix is not in reduced row-echelon form; there is not a 0 above and below the leading "1"s in the matrix.
d. $x + 8y + 6z = -4$
$y - 3z = 5$
$2z = -7$
$x + y + z = 0$
