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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}.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 |

if A is a square matrix of order 3, such that / adj.A / = 64 . then find / A' / .

|c b-x a|

|b a c-x|

^{3}- b^{3}-c^{3}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

A matrix of order 3X3 has determinant 5. What is the value of |3A|?

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 -ab1. 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) .state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????

| b^2 +c^2 ab ac |

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

| ca cb a^2+ b^2|

$\left|\begin{array}{cc}\mathrm{cos}15\xb0& \mathrm{sin}15\xb0\\ \mathrm{sin}75\xb0& \mathrm{cos}75\xb0\end{array}\right|$

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

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

^{2}1+z^{3}If det [ p b c

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

a b r]

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 !!

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 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

a

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

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

^{2}a^{2}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

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

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

| a^2+b^2/c c c |

| a b

^{2}+c^{2}/a a ||b b c

^{2}+a^{2}/b||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]

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}px+y x y

py+z y z = 0

0 px+y py+z

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

(a

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

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

^{2}+ a^{2})/b1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.

265 240 219

240 225 198

219 198 181

=0

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

Pls. answer

sin^2A cotA 1

sin^2B cotB 1 =0

sin^2C cotC 1

easy way to solve elementary row or column transformation

Show that

[y+z x y]

[z+x z x]

[x+y y z]

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

^{2}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?

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}|a b-c c+b

a+c b c-a

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

how to solve determinant of 4x4 matrix?

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

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}If A is an invertible matrix of order 3 and |A|=5, then find |adj A|

|sin(A+B+C) sin B cos C |

|-sinb 0 tan A | = 0,if A+B+c=pi?

|cos(A+B) -tan A 0 |

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.

^{9}B^{-1})2 1 7 3

prove that determinant of x x

^{2 }yzy y

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

^{2}xy| 5 4 a6 |

| a7 a8 a9 |

Then find the value of 21D .

[.] = greatest integer function

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|

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

prove that a+b+2c a b

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

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

example 32 in NCERT book

If 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!!!!!!

if A is a square matrix of order 3 and det adjA=64 find detA and det A

^{-1}HELP NEEDED URGENTIf the value of the third order determinant be 11,then what is value of the square of determinant formed by its cofactor?

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.

the r.d sharma 2007 editn. exercise. 6.2 pg. no.6.41, qwestn numb.1 pat no. 6 plz tell no hints available.............. :(((