Advertisements
Advertisements
प्रश्न
Answer the following question:
Evaluate determinant along second column
`|(1, -1, 2),(3, 2, -2),(0, 1, -2)|`
उत्तर
Let D = `|(1, -1, 2),(3, 2, -2),(0, 1, -2)|`
The expansion of the determinant D along second column is
D = – 1 (cofactor of – 1) + 2 (cofactor of 2) + 1 (cofactor of 1)
= `-1 xx (-1)^(1 + 2) |(3, -2),(0, -2)| + 2 xx (-1)^(2 + 2)|(1, 2),(0, -2)| + 1 xx (-1)^(2 + 3)|(1, 2),(3, -2)|`
= –1( –1) ( – 6 + 0) + 2 (1)( – 2 – 0) +1 ( –1)( –2 – 6)
= 1 ( – 6) + 2( – 2) – 1( – 8)
= –6 – 4 + 8
= – 2.
APPEARS IN
संबंधित प्रश्न
Find the minor and cofactor of element of the determinant
D = `|(2, -1, 3),(1, 2, -1),(5, 7, 2)|`
Evaluate A = `|(2, -3,5),(6, 0, 4),(1, 5, -7)|` Also find minor and cofactor of elements in the 2nd row of determinant and verify − a21.M21 + a22.M22 − a23.M23 = value of A
where M21, M22 , M23 are minor of a21 , a22, a23 and C21, C22, C23 are cofactor of a21, a22, a23
Evaluate A = `|(2, -3,5),(6, 0, 4),(1, 5, -7)|` Also find minor and cofactor of elements in the 2nd row of determinant and verify a21 C21 + a22 C22 + a23 C23 = value of A
where M21, M22, M23 are minors of a21, a22, a23 and
C21, C22, C23 are cofactors of a21, a22, a23.
Find the value of determinant expanding along third column
`|(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`
Answer the following question:
Find minor and cofactor of elements of the determinant:
`|(-1, 0, 4),(-2, 1, 3),(0, -4, 2)|`
Answer the following question:
Find minor and cofactor of elements of the determinant:
`|(1, -1, 2),(3, 0, -2),(1, 0, 3)|`
If Aij denotes the cofactor of the element aij of the determinant `|(2, -3, 5),(6, 0, 4),(1, 5, -7)|`, then value of a11A31 + a12A32 + a13A33 is ______.
The value of x obtained from the equation `|(x + a, b, c),(c, x + b, a),(a, b, x + c)|` = 0 will be ______.
The value of determinant `|((α^x + a^-x)^2, (α^x - α^-x)^2, 1),((β^x + β^-x)^2, (β^x - β^-x)^2, 1),((γ^x + γ^-x)^2, (γ^x - γ^-x)^2, 1)|`
