Concept of Elementary Row and Column Operation
Matrix and Determinant

79442 If \(A=\left|\begin{array}{ccc}1 & 3 & 1 \\ 2 & 1 & -1 \\ 3 & 0 & 1\end{array}\right|\), then \(\operatorname{rank}(A)\) is equal to

1 4
2 1
3 2
4 3
Matrix and Determinant

79443 If the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)\) and \(\left(x_{3}, y_{3}\right)\) are collinear, then the rank of the matrix
\(\left[\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & x_{3} & 1\end{array}\right]\) will always be less than

1 3
2 2
3 1
4 None of these
Matrix and Determinant

79444 If \(A\) is invertible matrix and \(B\) is any matrix, then

1 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{A})\)
2 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{B})\)
3 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{A})\)
4 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{B})\)
Matrix and Determinant

79445 Rank of the matrix
\(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) is

1 0
2 1
3 2
4 3
Matrix and Determinant

79442 If \(A=\left|\begin{array}{ccc}1 & 3 & 1 \\ 2 & 1 & -1 \\ 3 & 0 & 1\end{array}\right|\), then \(\operatorname{rank}(A)\) is equal to

1 4
2 1
3 2
4 3
Matrix and Determinant

79443 If the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)\) and \(\left(x_{3}, y_{3}\right)\) are collinear, then the rank of the matrix
\(\left[\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & x_{3} & 1\end{array}\right]\) will always be less than

1 3
2 2
3 1
4 None of these
Matrix and Determinant

79444 If \(A\) is invertible matrix and \(B\) is any matrix, then

1 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{A})\)
2 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{B})\)
3 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{A})\)
4 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{B})\)
Matrix and Determinant

79445 Rank of the matrix
\(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) is

1 0
2 1
3 2
4 3
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Matrix and Determinant

79442 If \(A=\left|\begin{array}{ccc}1 & 3 & 1 \\ 2 & 1 & -1 \\ 3 & 0 & 1\end{array}\right|\), then \(\operatorname{rank}(A)\) is equal to

1 4
2 1
3 2
4 3
Matrix and Determinant

79443 If the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)\) and \(\left(x_{3}, y_{3}\right)\) are collinear, then the rank of the matrix
\(\left[\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & x_{3} & 1\end{array}\right]\) will always be less than

1 3
2 2
3 1
4 None of these
Matrix and Determinant

79444 If \(A\) is invertible matrix and \(B\) is any matrix, then

1 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{A})\)
2 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{B})\)
3 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{A})\)
4 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{B})\)
Matrix and Determinant

79445 Rank of the matrix
\(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) is

1 0
2 1
3 2
4 3
Matrix and Determinant

79442 If \(A=\left|\begin{array}{ccc}1 & 3 & 1 \\ 2 & 1 & -1 \\ 3 & 0 & 1\end{array}\right|\), then \(\operatorname{rank}(A)\) is equal to

1 4
2 1
3 2
4 3
Matrix and Determinant

79443 If the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right)\) and \(\left(x_{3}, y_{3}\right)\) are collinear, then the rank of the matrix
\(\left[\begin{array}{lll}x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & x_{3} & 1\end{array}\right]\) will always be less than

1 3
2 2
3 1
4 None of these
Matrix and Determinant

79444 If \(A\) is invertible matrix and \(B\) is any matrix, then

1 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{A})\)
2 \(\operatorname{Rank}(\mathrm{AB})=\operatorname{Rank}(\mathrm{B})\)
3 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{A})\)
4 \(\operatorname{Rank}(\mathrm{AB})>\operatorname{Rank}(\mathrm{B})\)
Matrix and Determinant

79445 Rank of the matrix
\(A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]\) is

1 0
2 1
3 2
4 3