Advertisements
Advertisements
प्रश्न
Prove that `|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)| = 4a^2b^2c^2`
उत्तर
`|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|`
= `abc|(-a,b,c),(a,-b,c),(a,b,-c)|` ....(Take out a,b,c respectively from R1, R2 and R3)
= `a^2b^2c^2 |(-1,1,1),(1,-1,1),(1,1,-1)|` ...(Take out a,b,c respectively from C1, C2 and C3)
= `a^2b^2c^2 |(-1,1,1),(0,0,2),(0,2,0)|` ...`[("R"_2 -> "R"_2 + "R"_1),("R"_3 -> "R"_3 + "R"_1)]`
= a2b2c2 [-(0 – 4) + 0 + 0]
= 4a2b2c2
APPEARS IN
संबंधित प्रश्न
Find the minors and cofactors of all the elements of the following determinant.
`|(5,20),(0, -1)|`
Find the minors and cofactors of all the elements of the following determinant.
`|(1,-3,2),(4,-1,2),(3,5,2)|`
Prove that `|(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)|` = 0
The value of the determinant `[(a,0,0),(0,b,0),(0,0,c)]^2` is
Evaluation the following determination: `|(4,7),(-7, 0)| `
Evaluate the following determinant :
`|(a,h,g),(h,b,f),(g,f,c)|`
Without expanding evaluate the following determinant.
`|(1,a,a+c),(1,b,c+a),(1,c,a+b)|`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|= 29`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29
Find the value of x if `|(x, 2x, 3),(-1, 1, -4),(3, -3, 5)|` = 29
