Question

What is the determinant of the following matrix
0
1 0 0 0
100 1 0
100 2001 0
100 200 300 1​

Answer 1

Step-by-step explanation:

1 0 0 0

100 1 0 0

100 200 1 0

100 200 300 1

= 1 {1(1×1 - 0×300)}

= 1

Answer 2

Answer:

The determinant of the given matrix is 1

Step-by-step explanation:

- We are provided with a matrix

$\left[\begin{array}{cccc}1 & 0 & 0 & 0 \\100 & 1 & 0 & 0 \\100 & 200 & 1 & 0 \\100 & 200 & 300 & 1\end{array}\right]$

and we are asked to find the determinant of the above matrix

- If we observe closely, we find that the given matrix is a lower triangular matrix ( $A$ matrix in which all the elements above the main diagonal are zero) and we know that the determinant of a lower triangular matrix is the product of elements of the main diagonal

- So, the elements of the main diagonal are 1,1,1,1 and their product comes out to be 1

Therefore the determinant of the given matrix is 1