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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 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}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,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 ]

^{3}- b^{3}-c^{3}| b^2 +c^2 ab ac |

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

| ca cb a^2+ b^2|

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|?

prove without expanding that the determinant equals 0

b2c2 bc b-c

c2a2 ca c-a

a2b2 ab a-b

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) .If det [ p b c

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

a b r]

Given I

_{2}. Find determinant I_{2}. also find determinant 3I_{2}.state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????

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

|43 3 6|

|35 21 4|=0

|17 9 2|

py+z y z

0 px+y py+z

= 0

where p is any real number

In this kind of expression how to find the total number of terms and how to expand it?

|b+c a a |

| b c+a b |=4abc

| c c a+b |

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

(a

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

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

^{2}+ a^{2})/bfor any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?

[0 10]

prove using properties of determinants:

Xc1 Xc2 Xc3

Yc1 Yc2 Yc3 = xyz/12(x-y)(y-z)(z-x)

Zc1 Zc2 Zc3

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}how to provedeterminant x+y x x

5x+4y 4x 2x =x

^{3}10x+8y 8x 3x

265 240 219

240 225 198

219 198 181

=0

px+y x y

py+z y z = 0

0 px+y py+z

|x1 y1 2 |^2

|x2 y2 2| = 3a^4

|x3 y3 2|

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}1+x^{3 }y y

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

^{2}1+z^{3}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

easy way to solve elementary row or column transformation

IF |A|=2,where A is a 2x2 matrix ,find |adj A|.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}|evaluate without expansion

1 bc+ad b

^{2}c^{2}+a^{2}d^{2}1 ca+bd c

^{2}a^{2}+b^{2}d^{2}1 ab+cd a

^{2}b^{2}+c^{2}d^{2}ORUsing properties of determinants, prove the following :

$\left|\begin{array}{ccc}a& b-c& c-b\\ a-c& b& c-a\\ a-b& b-a& c\end{array}\right|=\left(a+b-c\right)\left(b+c-a\right)\left(c+a-b\right)$

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.

how to solve determinant of 4x4 matrix?

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

if A is an invertible matrix of order 3 and |A|=5 the find the value of |adjA|

sin^2A cotA 1

sin^2B cotB 1 =0

sin^2C cotC 1

a b-c c+b

a+c b c-a

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

using properties of determinants prove that :-2 *determinant[ (a b c) , (a' b' c') , (a" b" c")]=

determinant [(a+b b+c c+a) , (a'+b' b'+c' c'+a'),(a"+b" b"+c" c"+a")].

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

prove that determinant of x x

^{2 }yzy y

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

^{2}xyA 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.

^{2}+c^{2}ab ac | = 4a^{2}b^{2}c^{2}| ba c

^{2}+a^{2}bc | | ca cb a

^{2}+b^{2 |}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|

2/x-3/y+3/z=10

1/x+1/y+1/z=10

3/x-1/y+2/z=13

please explain with steps

prove that a+b+2c a b

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

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

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

| a b

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

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

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}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!!!!!!

A = [ 2 -3

3 4 ]

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

|3x-8 3 3|

| 3 3x-8 3| = 0

| 3 3 3x-8|

Is it the correct solution? If not how to do it?

a

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

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

^{2}a^{2}Prove that |x x+y x+2y| = 9y^2(x+y)

|x+2y x x+y|

|x+y x+2y x|