Properties of Determinants

IMPORTANT

Properties of Determinants: Overview

This topic covers concepts such as Properties of Determinants, Equality of Determinant and Its Transpose, Properties of Determinants under Elementary Transformations, Value of a Determinant Having Identical Rows/Columns, etc.

Important Questions on Properties of Determinants

HARD
IMPORTANT

Let A=abcd and B=pq00. Such that AB=B and a+d=5050. Find the value of ad-bc.

MEDIUM
IMPORTANT

Using properties of determinants, solve the following for x :

 x+axxxx+axxxx+a=0

EASY
IMPORTANT

The value of the following determinant would be:

 abbccabccaabcaabbc

HARD
IMPORTANT

The value of given determinant is

x+42x2x2xx+42x2x2xx+4

HARD
IMPORTANT

If  α, β, γ  are in A.P then, what would be the value of determinant  x-3x-4x-αx-2x-3x-βx-1x-2x-γ

HARD
IMPORTANT

If  α,β,γ  are in A.P then, what would be the value of determinant  x3x4xαx2x3xβx1x2xγ

HARD
IMPORTANT

Using properties of determinants, the solution for x:   | a+xaxax axa+xax axaxa+x |=0, would be :

MEDIUM
IMPORTANT

 a+bb+cc+ab+cc+aa+bc+aa+bb+c=

MEDIUM
IMPORTANT

Which of the following operation can prove,  sinαcosαcosα+δsinβcosβcosβ+δsinγcosγcosγ+δ=0

MEDIUM
IMPORTANT

Using properties of determinants, the value of   3aa+ba+cab3bcbacbc3c would be

EASY
IMPORTANT

       Let   ω= 1 2 +i 3 2 .  then the value of   | 111 11 ω 2 ω 2 1 ω 2 ω 4 | is equal to –
 

EASY
IMPORTANT

Let Ax1,y1, Bx2,y2, Cx3,y3, then find the area of given triangle.

Question Image

EASY
IMPORTANT

Find equation of line joining (-3,4) and (3,5) using determinants

EASY
IMPORTANT

Find equation of line joining (-2,4) and (2,5) using determinants

EASY
IMPORTANT

Find equation of line joining (-1,1) and (2,1) using determinants

EASY
IMPORTANT

Find equation of line joining (3,1) and (9,3) using determinants.

EASY
IMPORTANT

Find equation of line joining (1,2) and (3,6) using determinants

MEDIUM
IMPORTANT

Let A-1=120172120174120188. Then, 2A-2A-1 is equal to

EASY
IMPORTANT

Find equation of line passing through points 1,5 & 4,3 using determinants.

HARD
IMPORTANT

For all real numbers x, y and z, the determinant 2xxy-xzy2x+z+1xy-xz+yz-z21+y3x+12xy-2xz1+y is equal to