(A) Given the matrix $A = \begin{bmatrix} 2 & 3 & 1 & 4 \\ 0 & 1 & 2 & -1 \\ 0 & -2 & -4 & 2 \end{bmatrix}$.Apply the row operation $R_3 \to R_3 + 2R_

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(A) Given the matrix $A = \begin{bmatrix} 2 & 3 & 1 & 4 \\ 0 & 1 & 2 & -1 \\ 0 & -2 & -4 & 2 \end{bmatrix}$.Apply the row operation $R_3 \to R_3 + 2R_2$:$A \sim \begin{bmatrix} 2 & 3 & 1 & 4 \\ 0 & 1 & 2 & -1 \\ 0 & 0 & 0 & 0 \end{bmatrix}$.After performing the row operation,we observe that the third row becomes a zero row.The matrix is now in row-echelon form,and the number of non-zero rows is $2$.Therefore,the rank of the matrix $A$ is $2$.

Class 12 Mathematics 3-4. Matrices and Determinants Rank of Matrices , Some special determinants, differentiation and integration of determinants

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The rank of the matrix $A = \begin{bmatrix} 2 & 3 & 1 & 4 \\ 0 & 1 & 2 & -1 \\ 0 & -2 & -4 & 2 \end{bmatrix}$ is

A
$2$
B
$3$
C
$1$
D
Indeterminate

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3-4. Matrices and Determinants

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Rank of Matrices , Some special determinants, differentiation and integration of determinants

$A$ is an $m \times n$ matrix of rank $4$. If $A$ contains an $m$-th order non-singular submatrix and $A^T A$ is a $7 \times 7$ matrix, then the number of rows of $A$ is:

MediumTS EAMCET 2020

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If $D(x) = \begin{vmatrix} x - 1 & (x - 1)^2 & x^3 \\ x - 1 & x^2 & (x + 1)^3 \\ x & (x + 1)^2 & (x + 1)^3 \end{vmatrix}$,then the coefficient of $x$ in $D(x)$ is

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The rank of the matrix $A = \begin{bmatrix} 2 & 3 & 1 & 4 \\ 0 & 1 & 2 & -1 \\ 0 & -2 & -4 & 2 \end{bmatrix}$ is

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$A$ is an $m \times n$ matrix of rank $4$. If $A$ contains an $m$-th order non-singular submatrix and $A^T A$ is a $7 \times 7$ matrix, then the number of rows of $A$ is:

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