prove that: determinant | a b c a^2 b^2 c^2 bc ca ab|= (a-b)(b-c)(c-a)(ab+bc+ca)

If the H.M ofxandyis 2 then show that the points A (x, 2x), B(2y,y) and C(3, 3) are collinear.

using the properties of determinants, solve for x: |a+x a-x a-x a-x a+x a-x a-x a-x a+x| = 0

Urgent!!!!!

If p,q,r are not in G.P an d if detminant of given matrix is zero [ 1 q/p α+q/p 1 r/q α +r/q pα+q qα+r 0]then prove that pα^2+2pα+r=0

for a system of linear equations we know that if (adjA )B = 0 THEN THE SYSTEM MAY OR MAY NOT BE CONSISTENT.Discuss when it will become consistent and when inconsistent. is it necessary that if consistent than infinitely many solutions will be occurring in the above case?

Q) If a,b,c are the roots of the equation x*3+px+q=0,then find out the value of determinant.1+a 1 11 1+b 11 1 1+c.

log₃ 512 log₄3

log₃8 log₄9

For the matrix A = [ 2 -1 1 -1 2 -1 1 -1 2] verify that A^3 - 6A^2 + 9A - 4I = 0, Hence find A^-1

In IIT-JEE notes, determinanat chapter in which 2nd topic is "Properties of Determinants", where there are some videos in the ending of this topic regarding some question solving in that the 2nd video is about to find the value of the deteminant by given roots which i am not getting. So, kindly see that and help me.

Prove that the value of the determinant is real -7 5 + 3i 2/3 - 4i

5 - 3i 8 4 + 5i

2/3 + 4i 4 - 5i 9

Evaluate the following determinant :

1 4 9

4 9 16

9 16 25

if w is not equal to 1 then |A|= | 1 1+i+w² w²|

| 1-i -1 w²-1|

| -i -1+w-i -1 |

What is complex cube root of unity?

Respected sir/mam,

I am not getting the 2nd question(MCQ) video which is shown in the topic " Properties of determinants".

The question is like roots of a deteminanat is given and we have to find the values of the deteminant...???

so..plz kindly help me...!!!

The system of equations

2x - y + z = 0

x - 2y + z = 0

λx y + 2z = 0

has infinite number of nontrivial solutions for

1. λ = 1
2. λ = 5
3. λ = -5
4. no real value for λ

he system of equations

2x - y + z = 0

x - 2y + z = 0

λx - y + 2z = 0

has infinite number of nontrivial solutions for

1. λ = 1
2. λ = 5
3. λ = -5
4. no real value for λ

determinant - 67 19 21

39 13 14

81 24 26evaluate this ??

Prove that 1 1+p 1+p+q

2 3+2p 1+3p+2q = 1

3 6+3p 1+6p+3q

Let A be a non singular matrix of order 3 then det(adjA) is ?

If A is an invertible matrix of order 3 and det(A)=5. then find det(adj A).

great excuser faculty which always any time making excuses that due to paucity of time unable to solve ur query i dont lke this type of great excuse

solve my doubt

if a,b,c r positive and unequal show that this value is negative 3abc-( a cube+ b cube + c cube )

2- how to find adjoint of a and explain the best another way of solving this question example 32 of miscellaneous of ncert

explain singular and nonsingular matrix

Q.

Plzzz EXPLAIN...quickly. I need it urgently........

1.(k,0),(4,0),(0,2) 2.(-2,0),(0,4) ,(0,k)

The system of equations

2x - y + z = 0

x - 2y + z = 0

λx - y + 2z = 0

has infinite number of nontrivial solutions for

1. λ = 1
2. λ = 5
3. λ = -5
4. no real value for λ

prove, using the properties of determinants:

• determinant |b^2+c^2 a^2 a^2 b^2 c^2+a^2 b^2 c^2 c^2 a^2+b^2| = 4a^2b^2c^2 or is a perfect square

this q. is from iit meritnation ,practice question of determinant in maths.I can not be able to unterstand this question solution.so answere it in simple method.

Q.

det(A^-1) = ?

A) I B) 1/detA

show that the following determinant vanishes:

| a-b b-c c-a b-c c-a a-b c-a a-b b-c|

prove, using the properties of determinants:

• determinant |-a(b^2+c^2-a^2) 2b^3 2c^3 2a^3 -b(c^2+a^2-b^2) 2c^3 2a^3 2b^3 -c(a^2+b^2-c^2)| = abc(a^2+b^2+c^2)^3

Q.

Plzzz EXPLAIN...quickly. I need it urgently........

when we say solution of a system of equation is trivial what does it mean? is it same as unique solution?

For what value if x matrix A= [ x-1 1 1 1 x-1 1 1 1 x-1]is singular matrixx?

can there be a function which is discontinuous at a point but differentiable at that point? explain giving examples?

prove, using the properties of determinants:

• determinant |mC1mC2 mC3 nC1 nC2 nC3 pC1 pC2 pC3| = [mpn(m-n)(n-p)(p-m)]/12

WHAT IS THE RELATIONSHIP BETWEEN THE DETERMINANT OF A SQUARE AND INVERTIBLE MATRIX OF ORDER 3 AND ITS INVERSE? EXPLAIN HOW AND WITH EXAMPLES.

1.Can a determinant problem have different answers as per individual approach?

2.When to understand that a determinant will end up giving zero as the answer and some other value as the answer? Its tough to decipher this fact from the question saying "Evalute". Some problems give zero after evaluation while some others give values..

Will you Pls Help me out..

Do only square matrices have a MINOR ?

Please clear my doubt as soon as possible .

Thank You .

prove, using the properties of determinants:

• determinant |x+4 x x x x+4 x x x x+4| = 16(3x+4)

Prove, using the properties of determinants:

• determinant |(b+c)^2a^2bc (c+a)^2b^2ca (a+b)^2c^2ab| = (a-b) (b-c) (c-a) (a + b + c)(a^2+b^2+c^2)

Please explain the folloeing property of determinan with a suitable example :

the value of the determinant remains same, if we apply the operationR_i→R_i+kR_jorC_i→C_i+kC_j. That is,

PLEASE HELP SOON.

THANK YOU

prove, using the properties of determinants:

• determinant | a+b+c -c -b -c a+b+c -a -b -a a+b+c| = 2(a+b)(b+c)(c+a)