मराठी

By Using Properties of Determinants, Show That: |(X+4,2x,2x),(2x,X+4,2x),(2x , 2x, X+4)| = (5x + 4)(4-x)Sqrt2 - Mathematics

Advertisements
Advertisements

प्रश्न

By using properties of determinants, show that:

`|(x+4,2x,2x),(2x,x+4,2x),(2x , 2x, x+4)| = (5x + 4)(4-x)^2`

Advertisements

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants - Exercise 4.2 [पृष्ठ १२०]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 4 Determinants
Exercise 4.2 | Q 10.1 | पृष्ठ १२०

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 properties of determinants, prove that

`|[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3`


Using the property of determinants and without expanding, prove that:

`|(b+c, q+r, y+z),(c+a, r+p, z +x),(a+b, p+q, x + y )| = 2|(a,p,x),(b,q,y),(c, r,z)|`


By using properties of determinants, show that:

`|(1,a,a^2),(1,b,b^2),(1,c,c^2)| = (a - b)(b-c)(c-a)`


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)`


Evaluate `|(x, y, x+y),(y, x+y, x),(x+y, x, y)|`


Using properties of determinants, prove that:

`|(alpha, alpha^2,beta+gamma),(beta, beta^2, gamma+alpha),(gamma, gamma^2, alpha+beta)|` =  (β – γ) (γ – α) (α – β) (α + β + γ)


Using properties of determinants, prove that:

`|(1, 1+p, 1+p+q),(2, 3+2p, 4+3p+2q),(3,6+3p,10+6p+3q)| =  1`                 


Using properties of determinants show that

`[[1,1,1+x],[1,1+y,1],[1+z,1,1]] = xyz+ yz +zx+xy.`


Using properties of determinants, prove the following:

`|(a, b,c),(a-b, b-c, c-a),(b+c, c+a, a+b)| = a^3 + b^3 + c^3 - 3abc`.


Using properties of determinants, find the value of x for which
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`


Without expanding evaluate the following determinant:

`|(1, "a", "b" + "c"),(1, "b", "c" + "a"),(1, "c", "a" + "b")|`


Solve the following equation: `|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` =  0


Without expanding determinants, prove that `|("a"_1, "b"_1, "c"_1),("a"_2, "b"_2, "c"_2),("a"_3, "b"_3, "c"_3)| = |("b"_1, "c"_1, "a"_1),("b"_2, "c"_2, "a"_2),("b"_3, "c"_3, "a"_3)| = |("c"_1, "a"_1, "b"_1),("c"_2, "a"_2, "b"_2),("c"_3, "a"_3, "b"_3)|` 


Find the value (s) of x, if `|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0


Without expanding the determinants, show that `|(x"a", y"b", z"c"),("a"^2, "b"^2, "c"^2),(1, 1, 1)| = |(x, y, z),("a", "b", "c"),("bc", "ca", "ab")|`


Without expanding evaluate the following determinant:

`|(1, "a", "b" + "c"),(1, "b", "c" + "a"),(1, "c", "a" + "b")|`


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


Select the correct option from the given alternatives:

If x = –9 is a root of `|(x, 3, 7),(2, x, 2),(7, 6, x)|` = 0 has other two roots are


Select the correct option from the given alternatives:

Which of the following is correct


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


Evaluate: `|(3x, -x + y, -x + z),(x - y, 3y, z - y),(x - z, y - z, 3z)|`


Prove that: `|(y^2z^2, yz, y + z),(z^2x^2, zx, z + x),(x^2y^2, xy, x + y)|` = 0


Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz


The value of the determinant `abs ((alpha, beta, gamma),(alpha^2, beta^2, gamma^2),(beta + gamma, gamma + alpha, alpha + beta)) =` ____________.


A system of linear equations represented in matrix form Ax = 0, A is n × n matrix, has a non-zero solution if the determinant of A (i.e., det(A)) is


The A.M., H.M. and G.M. between two numbers are `144/15`, 15 and 12, but not necessarily in this order then, H.M., G.M. and A.M. respectively are


Which of the following is correct?


If `|(α, 3, 4),(1, 2, 1),(1, 4, 1)|` = 0, then the value of α is ______.


Without expanding determinant find the value of `|(10,57,107),(12,64,124),(15,78,153)|`


Without expanding determinants find the value of  `|(10,57,107),(12,64,124),(15,78,153)|`


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.


Without expanding determinants, find the value of  `|(10, 57, 107), (12, 64, 124), (15, 78, 153)|`


Without expanding evaluate the following determinant.

`|(1, a, b+c),(1, b, c+a),(1, c, a+b)|`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×