Teaching UP TGT Mock Test Series 2025 Mathematical Science Linear Algebra Matrix Representation of Linear Transformations
Which of the following matrices has the same row space as the matrix \(\left(\begin{array}{lll} 4 & 8 & 4 \\ 3 & 6 & 1 \\ 2 & 4 & 0 \end{array}\right)\) ?
1
\(\left(\begin{array}{lll} 1 & 2 & 0 \\ 0 & 0 & 1 \end{array}\right)\)
2
\(\left(\begin{array}{lll} 1 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)\)
3
\(\left(\begin{array}{lll} 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)\)
4
\(\left(\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right)\)