Can anyone please solve this 4x4 matrix with elementary row operation only? Step by step solution would be helpful and if its any helpful, answer to question is 20.Would really appreciate any help.
1 Answer
See below.
Explanation:
We need to find the determinant. If by elementary row operations we can get all elements except 1 in a row or column to be zero, then this makes finding the determinant much simpler. It should be remembered that multiplying any row or column and adding it to another row or column dosen't change the value of the determinant, but multiplying a row or column without adding it to another row or column does alter the value of the determinant.
For row operations the notation will be:
This is read as:
Row 2 is row 2 plus 2 times row 1 added to it.
Before we start we look to see where the least amount of operations to achieve our goal lie.
Now the first column has all zero elements except element
If we expand about the first row first column, we only need to find the 3 x 3 determinant shown in bold.
expanding this about the first row first column.
For the 4 x 4 determinant. expanding about first row first column.
So:
This idea is common practice when finding determinants of higher order.
