Advertisements
Advertisements
प्रश्न
Without expanding determinants, find the value of `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`
Advertisements
उत्तर
Let D = `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`
Applying C2 → C2 – C1, we get
D = `|(2014, 3, 1),(2020, 3, 1),(2023, 3, 1)|`
Taking (3) common from C2, we get
D = `3|(2014, 1, 1),(2020, 1, 1),(2023, 1, 1)|`
= 3(0) ...[∵ C2 and C3 are identical]
= 0
APPEARS IN
संबंधित प्रश्न
Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`
Using the property of determinants and without expanding, prove that:
`|(2,7,65),(3,8,75),(5,9,86)| = 0`
By using properties of determinants, show that:
`|(x,x^2,yz),(y,y^2,zx),(z,z^2,xy)| = (x-y)(y-z)(z-x)(xy+yz+zx)`
By using properties of determinants, show that:
`|(1,x,x^2),(x^2,1,x),(x,x^2,1)| = (1-x^3)^2`
Using properties of determinants, prove the following :
Using properties of determinants, prove that
`|[b+c , a ,a ] ,[ b , a+c, b ] ,[c , c, a+b ]|` = 4abc
Solve the following equation: `|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` = 0
Answer the following question:
Without expanding determinant show that
`|("b" + "c", "bc", "b"^2"c"^2),("c" + "a", "ca", "c"^2"a"^2),("a" + "b", "ab", "a"^2"b"^2)|` = 0
Answer the following question:
If `|("a", 1, 1),(1, "b", 1),(1, 1, "c")|` = 0 then show that `1/(1 - "a") + 1/(1 - "b") + 1/(1 - "c")` = 1
If A + B + C = 0, then prove that `|(1, cos"c", cos"B"),(cos"C", 1, cos"A"),(cos"B", cos"A", 1)|` = 0
Let P be any non-empty set containing p elements. Then, what is the number of relations on P?
If the ratio of the H.M. and GM. between two numbers a and bis 4 : 5, then a: b is
Without expanding evaluate the following determinant.
`|(1, a, a + c),(1, b, c + a),(1, c, a + b)|`
Evaluate the following determinant without expanding:
`|(5, 5, 5),(a, b, c),(b + c, c + a, a + b)|`
By using properties of determinants, prove that
`|(x+y, y+z, z+x),(z, x, y),(1, 1, 1)|` = 0
By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0
The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of the determinant of C2?
Without expanding evaluate the following determinant.
`|(1, a, b + c),(1, b, c + a),(1, c, a + b)|`
