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प्रश्न
Select the correct option from the given alternatives:
Which of the following is correct
विकल्प
Determinant is square matrix
Determinant is number associated to matrix
Determinant is number associated to square matrix
None of these
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उत्तर
Determinant is number associated to square matrix
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संबंधित प्रश्न
By using properties of determinants, show that:
`|(1,1,1),(a,b,c),(a^3, b^3,c^3)|` = (a-b)(b-c)(c-a)(a+b+c)
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`
Evaluate `|(1,x,y),(1,x+y,y),(1,x,x+y)|`
Using properties of determinants, prove that:
`|(x, x^2, 1+px^3),(y, y^2, 1+py^3),(z, z^2, 1+pz^2)|` = (1 + pxyz) (x – y) (y – z) (z – x), where p is any scalar.
Using properties of determinants, prove that
`|(sin alpha, cos alpha, cos(alpha+ delta)),(sin beta, cos beta, cos (beta + delta)),(sin gamma, cos gamma, cos (gamma+ delta))| = 0`
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 determinant prove that
`|(b+c , a , a), (b , c+a, b), (c, c, a+b)|` = 4abc
Solve for x : `|("a"+"x","a"-"x","a"-"x"),("a"-"x","a"+"x","a"-"x"),("a"-"x","a"-"x","a"+"x")| = 0`, using properties of determinants.
Without expanding determinants, find the value of `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`
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
Without expanding determinants show that
`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + 4|(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`
If `|("x"^"k", "x"^("k" + 2), "x"^("k" + 3)),("y"^"k", "y"^("k" + 2), "y"^("k" + 3)),("z"^"k", "z"^("k" + 2), "z"^("k" + 3))|` = (x - y) (y - z) (z - x)`(1/"x"+ 1/"y" + 1/"z") ` then
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
Evaluate: `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`
Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz
If A + B + C = 0, then prove that `|(1, cos"c", cos"B"),(cos"C", 1, cos"A"),(cos"B", cos"A", 1)|` = 0
Find the value of θ satisfying `[(1, 1, sin3theta),(-4, 3, cos2theta),(7, -7, -2)]` = 0
The value of determinant `|("a" - "b", "b" + "c", "a"),("b" - "a", "c" + "a", "b"),("c" - "a", "a" + "b", "c")|` is ______.
The determinant `|("b"^2 - "ab", "b" - "c", "bc" - "ac"),("ab" - "a"^2, "a" - "b", "b"^2 - "ab"),("bc" - "ac", "c" - "a", "ab" - "a"^2)|` equals ______.
The number of distinct real roots of `|(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx)|` = 0 in the interval `pi/4 x ≤ pi/4` is ______.
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 ______.
The determinant `abs (("a","bc","a"("b + c")),("b","ac","b"("c + a")),("c","ab","c"("a + b"))) =` ____________
If a, b, c are the roots of the equation x3 - 3x2 + 3x + 7 = 0, then the value of `abs((2 "bc - a"^2, "c"^2, "b"^2),("c"^2, 2 "ac - b"^2, "a"^2),("b"^2, "a"^2, 2 "ab - c"^2))` is ____________.
`abs(("x", -7),("x", 5"x" + 1))`
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
In a third order matrix B, bij denotes the element in the ith row and jth column. If
bij = 0 for i = j
= 1 for > j
= – 1 for i < j
Then the matrix is
The value of the determinant `|(1, cos(β - α), cos(γ - α)),(cos(α - β), 1, cos(γ - β)),(cos(α - γ), cos(β - γ), 1)|` is equal to ______.
If A, B and C are the angles of a triangle ABC, then `|(sin2"A", sin"C", sin"B"),(sin"C", sin2"B", sin"A"),(sin"B", sin"A", sin2"C")|` = ______.
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)|`
By using properties of determinant 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.
Without expanding evaluate the following determinant:
`|(1, a, b + c), (1, b, c + a), (1, c, a + b)|`
By using properties of determinant 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`
Without expanding the determinant, find the value of `|(10,57,107),(12,64,124),(15,78,153)|`
