Determine the rank of the matrix.
-$$\left[ \begin{array} { r r r r r }
1 & 0 & - 4 & 0 & 4 \
0 & 1 & - 3 & 0 & 4 \
0 & 0 & 0 & 1 & 1 \
0 & 0 & 0 & 0 & 0
\end{array} \right]$$
A)5
B)3
C)4
D)2

Question

Determine the rank of the matrix.
-$$\left[ \begin{array} { r r r r r } 
1 & 0 & - 4 & 0 & 4 \
0 & 1 & - 3 & 0 & 4 \
0 & 0 & 0 & 1 & 1 \
0 & 0 & 0 & 0 & 0
\end{array} \right]$$
A)5
B)3
C)4
D)2

Quizplus · Accepted Answer

The rank of a matrix is the number of non-zero rows in its row-echelon form. This matrix has 3 non-zero rows, so its rank is 3.

Determine the Rank of the Matrix [10−40401−3040001100000]\left[ \begin{array} { r r r r r } 1 & 0 & - 4 & 0 & 4 \\0 & 1 & - 3 & 0 & 4 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]​1000​0100​−4−300​0010​4410​​

Determine the Rank of the Matrix $\left[ \begin{array} { r r r r r } 1 & 0 & - 4 & 0 & 4 \\0 & 1 & - 3 & 0 & 4 \\0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 0\end{array} \right]$