edited by
20,661 views
29 votes
29 votes

The determinant of the matrix given below is

$$\begin{bmatrix}
0 &1  &0  &2 \\
 -1&  1&  1& 3\\
 0&0  &0  & 1\\
 1&  -2&  0& 1
\end{bmatrix}$$

  1. $-1$
  2. $0$
  3. $1$
  4. $2$
edited by

8 Answers

0 votes
0 votes
by simply interchanging rows of the determinant of the given matrix we easily calculate and found the value as -1 and hence option (A) is correct.
0 votes
0 votes
in this of  matrix  see in which row or column has maximum number of zero’s.

then its find cofactor then it will be the determinant of matrix.

eg int matrix A(3x4)=1 and all element in third row is zero except 1. so i take this matrix. now cofactor of (-1)^(3+4) *-1*-1=-1. hope it will help.
0 votes
0 votes

Let this matrix be A and cofactor of the elements be Cij

The determinant can be easily found by applying the cofactor multiplication on 3rd row(Since we have many zeroes which is easier for calculations)..

For Row 3,

det A =(-1)3+4.(1).det .—————Eqn 1

 

                                           

                                                                           Now, expanding the cofactor C34 we have

                                                                            (-1)1+2(1) det —————Eqn 2

                                                                          

                                                                             Again expanding the cofactor C12,we will have

                                                                              -1*0-(1)  ——————— Eqn 3                                                                        

                                                                             Combine all these 3 equation to have

                                                                             (-1)(1)*(-1)(1)*(-1)=-1*-1*-1 =-1

                                                                           

Answer:

Related questions

18 votes
18 votes
3 answers
1
Kathleen asked Sep 29, 2014
3,841 views
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$11$$-48$$0$$-24$
38 votes
38 votes
6 answers
2
Arjun asked Sep 23, 2014
9,195 views
Which one of the following does NOT equal $$\begin{vmatrix} 1 & x & x^{2}\\ 1& y & y^{2}\\ 1 & z & z^{2} \end{vmatrix} \quad ?$$$\begin{vmatrix} 1& x(x+1)& x+1\\ 1& y(y+1...
18 votes
18 votes
3 answers
3
0 votes
0 votes
1 answer
4
admin asked Apr 1, 2020
579 views
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiplied by $2,$ its determinant value becomes $40.$ The valu...