Course

ConceptProperties of Determinants

#### My Profile

My Profile [view full profile]

why create a profile on shaalaa.com?

1. Inform you about time table of exam.

2. Inform you about new question papers.

3. New video tutorials information.

1. Inform you about time table of exam.

2. Inform you about new question papers.

3. New video tutorials information.

clickto share

#### Question

Using properties of determinants, prove that

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

#### Solution

You need to to view the solution

Is there an error in this question or solution?

#### Appears in these question papers

#### Similar questions VIEW ALL

If ` f(x)=|[a,-1,0],[ax,a,-1],[ax^2,ax,a]| ` , using properties of determinants find the value of *f*(2*x*) − *f*(*x*).

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`

Using properties of determinants, prove that

`|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3`

Using properties of determinants, prove that

`|[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|`

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`

#### Reference Material

Solution for concept: Properties of Determinants. For the courses 12th CBSE (Arts), 12th CBSE (Commerce), 12th CBSE (Science)