English

Using Properties of Determinants, Prove that Matrix (X,X+Y,X+2y),(X+2y, X,X+Y),(X+Y, X+2y, X) = 9ysquare2(X + Y)` - Mathematics

Advertisements
Advertisements

Question

Using properties of determinants, prove that |xx+yx+2yx+2yxx+yx+yx+2yx|=9y2(x+y)

Solution

shaalaa.com
  Is there an error in this question or solution?
2016-2017 (March) Delhi Set 1

RELATED QUESTIONS

By using properties of determinants, show that:

|111abca3b3c3| = (a-b)(b-c)(c-a)(a+b+c)


Evaluate |1xy1x+yy1xx+y|


Using properties of determinants, prove that 

|a2+2a2a+112a+1a+21331|=(a-1)3


Using properties of determinants, prove that |111+3x1+3y1111+3z1|=9(3xyz+xy+ yz+zx)


Using properties of determinants, prove the following:

|x2+1xyxzxyy2+1yzxzyzz2+1|=1+x2+y2+z2 .

Solve for x : |a+xa-xa-xa-xa+xa-xa-xa-xa+x|=0, using properties of determinants. 


Evaluate the following determinants:

|x-1xx-20x-2x-300x-3|=0


By using properties of determinants, prove that |x+yy+zz+xzxy111| = 0.


Without expanding the determinants, show that |xaybzca2b2c2111|=|xyzabcbccaab|


Using properties of determinant show that

|1logxylogxzlogyx1logyzlogzxlogzy1| = 0


Solve the following equation: 

|x+2x+6x-1x+6x-1x+2x-1x+2x+6| = 0


Select the correct option from the given alternatives:

The system 3x – y + 4z = 3, x + 2y – 3z = –2 and 6x + 5y + λz = –3 has at least one Solution when


Select the correct option from the given alternatives:

If |6i-3i143i-1203i| = x + iy then


Answer the following question:

Evaluate |2354006001000484718| by using properties


Evaluate: |3x-x+y-x+zx-y3yz-yx-zy-z3z|


The determinant |b2-abb-cbc-acab-a2a-bb2-abbc-acc-aab-a2| equals ______.


The determinant |abca(b + c)bacb(c + a)cabc(a + b)|= ____________


If a, b, c are the roots of the equation x3 - 3x2 + 3x + 7 = 0, then the value of |2bc - a2c2b2c22ac - b2a2b2a22ab - c2| is ____________.


If the ratio of the H.M. and GM. between two numbers a and bis 4 : 5, then a: b is


f:{1,2,3){4,5} is not a function, if it is defined by which of the following?


The value of the determinant |60-1214113| is ______.


Without expanding determinant find the value of |105710712641241578153|


By using properties of determinant prove that

|x+yy+zz+xzxy111| = 0 


By using properties of determinant prove that |x+yy+zz+xzxy111|=0


By using properties of determinant prove that |x+yy+zz+xzxy111|=0


Without expanding determinant find the value of |105710712641241578153|


By using properties of determinants, prove that 

|x+yy+zz+xzxy111| = 0 


Without expanding evaluate the following determinant.

|1ab+c1bc+a1ca+b|


if |abcmnpxyz|=k, then what is the value of |6a2b2c3mnp3xyz|?


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 determinant of C2?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.