The rank of the matrix A=begin{bmatrix} 1 & - | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given matrix $A = \begin{bmatrix} 1 & -1 & 0 & -2 \ -4 & 4 & 0 & 8 \ -2 & 1 & 2 & 4 \end{bmatrix}$.We apply elementary row operations to transfo

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) Given matrix $A = \begin{bmatrix} 1 & -1 & 0 & -2 \ -4 & 4 & 0 & 8 \ -2 & 1 & 2 & 4 \end{bmatrix}$.We apply elementary row operations to transform the matrix into row echelon form.Step $1$: Apply $R_2 ightarrow R_2 + 4R_1$ and $R_3 ightarrow R_3 + 2R_1$.$A \sim \begin{bmatrix} 1 & -1 & 0 & -2 \ 0 & 0 & 0 & 0 \ 0 & -1 & 2 & 0 \end{bmatrix}$.Step $2$: Swap $R_2$ and $R_3$ $(R_2 \leftrightarrow R_3)$.$A \sim \begin{bmatrix} 1 & -1 & 0 & -2 \ 0 & -1 & 2 & 0 \ 0 & 0 & 0 & 0 \end{bmatrix}$.The matrix is now in row echelon form. The number of non-zero rows is $2$.Therefore,the rank of matrix $A$ is $2$.

The rank of the matrix $A=\begin{bmatrix} 1 & -1 & 0 & -2 \\ -4 & 4 & 0 & 8 \\ -2 & 1 & 2 & 4 \end{bmatrix}$ is

Similar Questions

If $y = \sin(px)$ and $y_n$ is the $n^{th}$ derivative of $y$,then $\left| \begin{array}{ccc} y & y_1 & y_2 \\ y_3 & y_4 & y_5 \\ y_6 & y_7 & y_8 \end{array} \right|$ is equal to:

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

If $f(x) = \begin{vmatrix} 2 \cos^4 x & 2 \sin^4 x & 3 + \sin^2 2x \\ 3 + 2 \cos^4 x & 2 \sin^4 x & \sin^2 2x \\ 2 \cos^4 x & 3 + 2 \sin^4 x & \sin^2 2x \end{vmatrix}$,then $\frac{1}{5} f'(0)$ is equal to:

If $A = \begin{vmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{vmatrix}$ and $B = \begin{vmatrix} x & 1 \\ 1 & x \end{vmatrix}$,then $\frac{dA}{dx}$ is equal to

If $f: N \to Z$ is defined by $f(n) = \det \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3(2k+1) & 3(k+2)+1 \end{vmatrix}$, where $k \in N$ and $\sum_{n=1}^k f(n) = 98$, then $k$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module