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Syllabus

Using properties of determinants prove that -

(b+c)

^{2}....a^{2}........a^{2}b

^{2}.....(c+a)^{2.}.....b^{2}=2abc(a+b+c)^{3}c

^{2}.....c^{2}.......(a+b)^{2}In this ques.. i just want to know tht after applying C

_{1}→ C_{1}-C_{2}, C_{2}→ C_{2}-C_{3}in this ques how can i take (a+b+c) common from C

_{1}and C_{2}.if A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .

Prove that

| (b+c)^2 a^2 a^2 |

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

| c^2 c^2 (a+b)^2 |

^{3}- b^{3}-c^{3}Let {D

_{1},D_{2},D_{3},........,D_{n}} be the set of all third order determinants that can be made with the distinct non-zero real number a_{1},a_{2},a_{3},........,a_{0},then,the answer is - summation i=1 to n D

_{i }= 0 .How?Please explain me briefly.

If a,b,c, all positive ,are pth,qth and rth terms of G.P. , prove that determinant [ log a p 1

log b q 1 = 0

log c r 1 ]

if a is a square matrix of order 3 and / 3A / = k/A/ find value of k? pls fast plss

Prove that the following determinant is equal to (ab + bc + ca)

^{3 :}-bc b

^{2}+ bc c^{2}+ bca

^{2}+ ac -ac c^{2}+ aca

^{2}+ ab b^{2}+ ab -abA matrix of order 3X3 has determinant 5. What is the value of |3A|?

Difference between cramer's rule and Matrix method.....and when to use which one.....

Solve:

(i) x+y-2z =0 (ii)2x+3y+4z =0 (iii)3x+y+z =0 (iv) x+2y-3z = -4

2x+y-3z =0 x+y+z =0 x-4y+3z =02x+3y+2z =2

5x+4y-9z =0 2x-y+3z =0 2x+5y-2z =0 3x-3y-4z =11

1. Using properties of determinants, prove the following:

| x y z

x

^{2}y^{2}z^{2}x

^{3}y^{3}z^{3 | = }xyz(x - y)(y - z)(z - x) .2. Using properties of determinants, prove the following :

| x x

^{2}1+px^{3}y y

^{2}1+py^{3}z z

^{2}1+pz^{3}| = (1+ pxyz)(x - y)(y - z)(z - x) .{1 a2+bc a3

1 b2+ca b3

1 c2+ab c3} = -(a-b) (b-c) (c-a) (a2 +b2+c2) using properties of determinannts solve

If det [ p b c

a q c = 0 then find (p/p-a) + (q/q-b) + (r/r-c)

a b r]

|x p q|

|p x q| =(x-p)(x^2+px-2q^2)

|q q x|

PROVE THAT THE DETERMINANT

b

^{2}+c^{2}ab acab c

^{2}+a^{2 }bcac bc a

^{2}+b^{2}is equal to 4a

^{2}b^{2}c^{2}state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????

Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

| b^2 +c^2 ab ac |

| ab c^2+a^2 bc |=4a^2b^2c^2

| ca cb a^2+ b^2|

Using properties of determinants, solve the following for x :

x-2 2x-3 3x-4

x-4 2x-9 3x-16 =0

x-8 2x-27 3x-64

prove without expanding that the determinant equals 0

b2c2 bc b-c

c2a2 ca c-a

a2b2 ab a-b

py+z y z

0 px+y py+z

= 0

where p is any real number

Show that

[y+z x y]

[z+x z x]

[x+y y z]

=(x +y+z) (x-z)

^{2}|b+c a a |

| b c+a b |=4abc

| c c a+b |

for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?

[0 10]

if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..

Please solve the following determinant based question | (y+z)^2 xy zx |

| xy (x+z)^2 yz | = 2xyz(x+y+z)^3 .

| xz yz (x+y)^2 |

Please give the answer fast !!

Using properties of determinats, prove that

a

^{2 }2ab b^{2}b

^{2 }a^{2 }2ab2ab b

^{2 }a^{2 }= (a

^{3}+ b^{3})^{2}265 240 219

240 225 198

219 198 181

=0

2.For what value of k the points (5,5),(k,1)and(11,7)are collinear(ans is k=-7)

if A is a square matrix and det A = 2 , then write the value of det AA' where A' is the transpose of matrix A.

px+y x y

py+z y z = 0

0 px+y py+z

A = [ 2 -3

3 4 ]

satisfies the equation x^2 - 6x + 17 = 0. Hence find A^-1.

1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ?

|2 y 3|

|1 1 z|

xyz=80 and 3x+2y+10z=20

Find value of A(adjA)

An amount of Rs. 10,000 is put into three investments at the rate of 10,12 and 15 per cent per annum. The combined income is Rs. 1,310 and the combined income of the first and the second investment is Rs. 190 short of the income from the third.

i) Represent the above situation by matrix equation and form the linear equation using multiplication.

ii) Is it possible to solve the system of equations so obtained using matrices?

Show that the elements along the main diagonal of a skew symmetric matrix are all zero.

Pls. answer

5 -2]

write A Inverse in terms of A

easy way to solve elementary row or column transformation

prove that the 3x3 determinant :

| 1+a

^{2}-b^{2}2ab -2b || 2ab 1-a

^{2}+b^{2}2a | = (1+a^{2}+b^{2})^{3 }| 2b -2a 1-a

^{2}-b^{2}|= 2(a+b)(b+c)(c+a)

how to solve determinant of 4x4 matrix?

If A is an invertible matrix of order 3 and |A|=5, then find |adj A|

subscriber. She proposes to increase the annual subscription charges and it is believed that for

every increase of Re 1, one subscriber will discontinue. What increase will bring maximum

income to her? Make appropriate assumptions in order to apply derivatives to reach the

solution. Write one important role of magazines in our lives.

a b-c c+b

a+c b c-a

a-b b+a c =(a+b+c)(a^2+b^2+c^2)

|x1 y1 2 |^2

|x2 y2 2| = 3a^4

|x3 y3 2|

prove that determinant of x x

^{2 }yzy y

^{2}zx = (x-y)(y-z)(z-x)(xy+yz+zx)z z

^{2}xy^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}A is a square matrix of order 3 and det. A = 7. Write the value of adj A.

Please give me any formula or method for calculating this problem.

Using the properties of determinants ,show that..

1 x+y x2+y2

1 y+z y2+z2

1 z+x z2+x2

=(x-y)(y-z)(z-x)

(((x2,y2,z2 are x square,y square and z square respectively)))

(meritnation exprt please ans .....)

(a

^{2}+ b^{2})/c c ca (b

^{2}+ c^{2})/a a = 4abcb b ( c

^{2}+ a^{2})/bprove that a+b+2c a b

c b+c+2a b = 2( a+b+c)

^{3}c a c+a+2b

if a,b,c are all positive and are pth,qth,rth terms of a G.P, then show that determinant

|log a p 1|

| log c r 1|

iii). $\left[\begin{array}{ccc}x+1& -3& 4\\ -5& x+2& 2\\ 4& 1& x-6\end{array}\right]$

Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}abIf x + y + z = 0, prove that|xa yb zc| |a b c||yc za xb|= xyz |c a b||zb xc ya| |b c a|

Iwant the answer within 2 hours.Please!!!!!!

^{2}1+x^{3 }y y

^{2}1+y^{3}= 0 , then show that 1+xyz = 0 ?z z

^{2}1+z^{3}if a ,b,c are the lengths of sides BC ,CA,AB of a triangle ABC proof that

BC+CA+AB=0 and deduce that

a/sinA=b/sinB=c/sinC

refer r.d 25.1 ques 20 and pls answer fast pls of all ques that r asked

a

^{2}2ab b^{2}b

^{2}a^{2}2ab = (a^{3}+b^{3})^{2}2ab b

^{2}a^{2}