If the matrix A=left[begin{array}{cccc}1 & 2 | vedclass

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

Question

(B) Given,$A=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \ 2 & 4 & 3 & 2 \ 3 & 2 & 1 & 3 \ 6 & 8 & 7 & \alpha\end{array}ight]$.Applying row operations

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Given,$A=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \ 2 & 4 & 3 & 2 \ 3 & 2 & 1 & 3 \ 6 & 8 & 7 & \alpha\end{array}ight]$.Applying row operations $R_2 ightarrow R_2-2R_1$,$R_3 ightarrow R_3-3R_1$,and $R_4 ightarrow R_4-6R_1$:$A \sim \left[\begin{array}{cccc}1 & 2 & 3 & 0 \ 0 & 0 & -3 & 2 \ 0 & -4 & -8 & 3 \ 0 & -4 & -11 & \alpha\end{array}ight]$.Applying $R_4 ightarrow R_4-R_3$:$A \sim \left[\begin{array}{cccc}1 & 2 & 3 & 0 \ 0 & 0 & -3 & 2 \ 0 & -4 & -8 & 3 \ 0 & 0 & -3 & \alpha-3\end{array}ight]$.Applying $R_4 ightarrow R_4-R_2$:$A \sim \left[\begin{array}{cccc}1 & 2 & 3 & 0 \ 0 & 0 & -3 & 2 \ 0 & -4 & -8 & 3 \ 0 & 0 & 0 & \alpha-5\end{array}ight]$.Since the rank of matrix $A$ is $3$,the last row must be a zero row.Therefore,$\alpha-5=0$,which implies $\alpha=5$.

If the matrix $A=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\ 2 & 4 & 3 & 2 \\ 3 & 2 & 1 & 3 \\ 6 & 8 & 7 & \alpha\end{array}\right]$ is of rank $3$,then $\alpha$ equals to

Similar Questions

If $A = [a_{ij}]$,$1 \leq i, j \leq n$ with $n \geq 2$ and $a_{ij} = i + j$ is a matrix,then the rank of $A$ is

If ${D_p} = \begin{vmatrix} p & 15 & 8 \\ p^2 & 35 & 9 \\ p^3 & 25 & 10 \end{vmatrix}$,then ${D_1} + {D_2} + {D_3} + {D_4} + {D_5} = $

If the rank of the matrix $A=\begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix}$ is $2$ and $k$ is a real number,then $k$ is a root of the following quadratic equation:

If $y = \sin(mx)$,then the value of $\left| \begin{array}{ccc} y & y_1 & y_2 \\ y_3 & y_4 & y_5 \\ y_6 & y_7 & y_8 \end{array} \right|$ (where subscripts of $y$ denote the order of derivative) is:

In a matrix $A$,if all the sub-matrices of order $k$ are singular and there is at least one non-singular sub-matrix of order $r$ $(r < k)$,then the rank $(\rho)$ of the matrix $A$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module