Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$
(N/A) The given determinant is $\Delta = \left|\begin{array}{cc}2 & -4 \\ 0 & 3\end{array}\right|$.
The minor of an element $a_{ij}$ is denoted by $M_{ij}$.
For $a_{11} = 2$,$M_{11} = 3$.
For $a_{12} = -4$,$M_{12} = 0$.
For $a_{21} = 0$,$M_{21} = -4$.
For $a_{22} = 3$,$M_{22} = 2$.
The cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ and is given by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (1)(3) = 3$.
$A_{12} = (-1)^{1+2} M_{12} = (-1)(0) = 0$.
$A_{21} = (-1)^{2+1} M_{21} = (-1)(-4) = 4$.
$A_{22} = (-1)^{2+2} M_{22} = (1)(2) = 2$.
The minor of an element $a_{ij}$ is denoted by $M_{ij}$.
For $a_{11} = 2$,$M_{11} = 3$.
For $a_{12} = -4$,$M_{12} = 0$.
For $a_{21} = 0$,$M_{21} = -4$.
For $a_{22} = 3$,$M_{22} = 2$.
The cofactor of an element $a_{ij}$ is denoted by $A_{ij}$ and is given by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (1)(3) = 3$.
$A_{12} = (-1)^{1+2} M_{12} = (-1)(0) = 0$.
$A_{21} = (-1)^{2+1} M_{21} = (-1)(-4) = 4$.
$A_{22} = (-1)^{2+2} M_{22} = (1)(2) = 2$.
Explore More
Similar Questions
If $A = \begin{bmatrix} 3 & 5 \\ 2 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 17 \\ 0 & -10 \end{bmatrix}$,then $|AB|$ is equal to
Easy
View SolutionIf $A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$,where $A_{21}, A_{22}, A_{23}$ are cofactors of $a_{21}, a_{22}, a_{23}$ respectively,then the value of $a_{21} A_{21} + a_{22} A_{22} + a_{23} A_{23} = $
Match the following elements of the matrix $A = \left[\begin{array}{ccc} 1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6 \end{array}\right]$ with their co-factors and choose the correct answer.
Element Co-factor $A$. $-1$ $(1)$ $-2$ $B$. $1$ $(2)$ $32$ $C$. $3$ $(3)$ $4$ $D$. $6$ $(4)$ $6$ $(5)$ $-6$
| Element | Co-factor |
| $A$. $-1$ | $(1)$ $-2$ |
| $B$. $1$ | $(2)$ $32$ |
| $C$. $3$ | $(3)$ $4$ |
| $D$. $6$ | $(4)$ $6$ |
| $(5)$ $-6$ |
Let $A = [a_{ij}] = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix}$. If $A_{ij}$ is the cofactor of $a_{ij}$,$C_{ij} = \sum_{k=1}^2 a_{ik} A_{jk}$,$1 \leq i, j \leq 2$,and $C = [C_{ij}]$,then $8|C|$ is equal to:
DifficultJEE MAIN 2025
View SolutionUsing cofactors of elements of the third column,evaluate $\Delta = \left| \begin{array}{ccc} 1 & x & yz \\ 1 & y & zx \\ 1 & z & xy \end{array} \right|$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo