determinants using properties of determinants Example [[1977,1979,1981],[1940,1943,1946],[10,17,24]]

Find value of determinant using properties of determinants ...
`[[1977,1979,1981],[1940,1943,1946],[10,17,24]]`

Solution:

`A=`

1977	1979	1981
1940	1943	1946
10	17	24

Now, `C_2=C_2 - C_1` and `C_3=C_3 - C_2`

`=`

1977	2	2
1940	3	3
10	7	7

Here `C_2=C_3`, So value of the determinant is 0

`=0`

Method-2: Determinant by expanding cofactors

`|A|`

`1977`	`1979`	`1981`
`1940`	`1943`	`1946`
`10`	`17`	`24`

`1977`

	`1943`	`1946`
	`17`	`24`

`-1979`

	`1940`	`1946`
	`10`	`24`

`+1981`

	`1940`	`1943`
	`10`	`17`

`=1977 xx (1943 × 24 - 1946 × 17) -1979 xx (1940 × 24 - 1946 × 10) +1981 xx (1940 × 17 - 1943 × 10)`

`=1977 xx (46632 -33082) -1979 xx (46560 -19460) +1981 xx (32980 -19430)`

`=1977 xx (13550) -1979 xx (27100) +1981 xx (13550)`

`= 26788350 -53630900 +26842550`

`=0`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here

4. Example `[[1977,1979,1981],[1940,1943,1946],[10,17,24]]`