determinants using properties of determinants Example [[201,210,220],[151,155,140],[50,55,80]]

1. Find value of determinant using properties of determinants ...
`[[201,210,220],[151,155,140],[50,55,80]]`

Solution:

`A=`

201	210	220
151	155	140
50	55	80

Now, `R_1=R_1 - R_2`

`=`

50	55	80
151	155	140
50	55	80

Here `R_3=R_1`, So value of the determinant is 0

`=0`

Method-2: Determinant by expanding cofactors

`|A|`

`201`	`210`	`220`
`151`	`155`	`140`
`50`	`55`	`80`

`201`

	`155`	`140`
	`55`	`80`

`-210`

	`151`	`140`
	`50`	`80`

`+220`

	`151`	`155`
	`50`	`55`

`=201 xx (155 × 80 - 140 × 55) -210 xx (151 × 80 - 140 × 50) +220 xx (151 × 55 - 155 × 50)`

`=201 xx (12400 -7700) -210 xx (12080 -7000) +220 xx (8305 -7750)`

`=201 xx (4700) -210 xx (5080) +220 xx (555)`

`= 944700 -1066800 +122100`

`=0`

2. 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`

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1. Example `[[201,210,220],[151,155,140],[50,55,80]]`