Advertisements
Advertisements
प्रश्न
Answer the following question:
Evaluate `|(101, 102, 103),(106, 107, 108),(1, 2, 3)|` by using properties
Advertisements
उत्तर
Let D = `|(101, 102, 103),(106, 107, 108),(1, 2, 3)|`
By C3 – C2, we get,
D = `|(101, 102, 1),(106, 107, 1),(1, 2, 1)|`
By C2 – C1, we get,
D = `|(101, 1, 1),(106, 1, 1),(1, 1, 1)|`
= 0 .......[∵ C2 ≡ C3]
APPEARS IN
संबंधित प्रश्न
Using properties of determinants, show that ΔABC is isosceles if:`|[1,1,1],[1+cosA,1+cosB,1+cosC],[cos^2A+cosA,cos^B+cosB,cos^2C+cosC]|=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:
`|(a-b-c, 2a,2a),(2b, b-c-a,2b),(2c,2c, c-a-b)| = (a + b + c)^2`
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 that
`|(a^2 + 2a,2a + 1,1),(2a+1,a+2, 1),(3, 3, 1)| = (a - 1)^3`
Using properties of determinants, prove that `|(x,x+y,x+2y),(x+2y, x,x+y),(x+y, x+2y, x)| = 9y^2(x + y)`
Using properties of determinants, prove that:
`|(1+a^2-b^2, 2ab, -2b),(2ab, 1-a^2+b^2, 2a),(2b, -2a, 1-a^2-b^2)| = (1 + a^2 + b^2)^3`
Using properties of determinants, show that `|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc.
If `|(4 + x, 4 - x, 4 - x),(4 - x, 4 + x, 4 - x),(4 - x, 4 - x, 4 + x)|` = 0, then find the values of x.
Find the value (s) of x, if `|(1, 2x, 4x),(1, 4, 16),(1, 1, 1)|` = 0
By using properties of determinants, prove that `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` = 0.
Without expanding evaluate the following determinant:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
Without expanding evaluate the following determinant:
`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`
Using properties of determinant show that
`|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` = 0
If `|(4 + x, 4 - x, 4 - x),(4 - x,4 + x,4 - x),(4 - x,4 - x, 4 + x)|` = 0, then find the values of x.
Select the correct option from the given alternatives:
`|("b" + "c", "c" + "a", "a" + "b"),("q" + "r", "r" + "p", "p" + "q"),(y + z, z + x, x + y)|` =
Answer the following question:
Without expanding determinant show that
`|(0, "a", "b"),(-"a", 0, "c"),(-"b", -"c", 0)|` = 0
Evaluate: `|(x + 4, x, x),(x, x + 4, x),(x, x, x + 4)|`
Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz
The value of determinant `|("a" - "b", "b" + "c", "a"),("b" - "a", "c" + "a", "b"),("c" - "a", "a" + "b", "c")|` is ______.
If A, B and C are angles of a triangle, then the determinant `|(-1, cos"C", cos"B"),(cos"C", -1, cos"A"),(cos"B", cos"A", -1)|` is equal to ______.
The maximum value of Δ = `|(1, 1, 1),(1, 1 + sin theta, 1),(1 + cos theta, 1, 1)|` is ______. (θ is real number)
If x, y, z ∈ R, then the value of determinant `|((2x^2 + 2^(-x))^2, (2^x - 2^(-x))^2, 1),((3^x + 3^(-x))^2, (3^x -3^(-x))^2, 1),((4^x + 4^(-x))^2, (4^x - 4^(-x))^2, 1)|` is equal to ______.
Let Δ = `|("a", "p", x),("b", "q", y),("c", "r", z)|` = 16, then Δ1 = `|("p" + x, "a" + x, "a" + "p"),("q" + y, "b" + y, "b" + "q"),("r" + z, "c" + z, "c" + "r")|` = 32.
The value of the determinant `abs ((alpha, beta, gamma),(alpha^2, beta^2, gamma^2),(beta + gamma, gamma + alpha, alpha + beta)) =` ____________.
Let P be any non-empty set containing p elements. Then, what is the number of relations on P?
Let 'A' be a square matrix of order 3 × 3, then |KA| is equal to:
In a triangle the length of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be ______.
Without expanding determinants find the value of `|(10,57,107),(12,64,124),(15,78,153)|`
Evaluate the following determinant without expanding:
`|(5, 5, 5),(a, b, c),(b + c, c + a, a + b)|`
By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0
Without expanding determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`
By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0
Without expanding evaluate the following determinant.
`|(1, a, b+c),(1, b, c+a),(1, c, a+b)|`
