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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}.^{3}- b^{3}-c^{3}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 |

Without expanding the determinant , show that

|1 a a| |^{2}1 bc b+c||1 b b^{2}|=|1 ca c+a||1 c c| |^{2}1 ab a+b|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

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) .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 -ab(a

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

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

^{2}+ a^{2})/bA matrix of order 3X3 has determinant 5. What is the value of |3A|?

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

Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}abIf det [ p b c

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

a b r]

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

|b+c a a |

| b c+a b |=4abc

| c c a+b |

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.....

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

[0 10]

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}^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}265 240 219

240 225 198

219 198 181

=0

px+y x y

py+z y z = 0

0 px+y py+z

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 ?

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?

solve the system of equations

x-y+2z=1

2y-3z=1

3x-2y+4z=2

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

Pls. answer

Using the properties of determinants, prove that:

1 x x

^{3}1 y y

^{3 }=(x-y) (y-z) (z-x) (x+y+z)1 z z

^{3}easy way to solve elementary row or column transformation

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.

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}|5.Three schools A, B and C want to award their selected students for the values of honesty, regularity and hard work. Each school decided to award a sum of Rs. 2500, Rs. 3100, Rs. 5100 per student for the respective values. The number of students to be awarded by the three schools as given below:A = 50500, 40800, 41600

If one root of

7 6 x

2 x 2

x 3 7

=0 is x =-9,Find the other roots

(ans is 2,7)

how to solve determinant of 4x4 matrix?

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

For what values of a and b, the following system of equations is consistent?

x+y+z=6

2x+5y+az=b

x+2y+3z=14 [by matrix method]

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)

If a,b, and c are all non-zero and |1+a 1 1| = 0, then prove that 1/a+1/b+1/c+1=0

|1 1+b 1|

|1 1 1+c|

|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}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.

{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

The sum of three numbers is 2 . if twice the second number is added to the sum of the first and third , the sum is 1.by adding second and third number to five times the first number,we get 6 . find the three numbers by using matrices.

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 this:If $A=\left[\begin{array}{ccc}4& -5& -11\\ 1& -3& 1\\ 2& 3& -7\end{array}\right]$ , find A

^{-1}. Using A^{-1},Solve the system of linear equations :

4x - 5y - 11z = 12, x - 3y + z = 1, 2x + 3y - 7z = 2.

prove that a+b+2c a b

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

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

Is Cramer's rule allowed in matrices in cbse..? my teacher gve a question :

solve the foll. using Cramer's rule:

x+y+z=11 ; 2x-6y-z=0 ; 3x+4y+2z=0.

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

Using determinants prove the following points are collinear..

A = [ 2 -3

3 4 ]

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

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!!!!!!

|10! 11! 12!|

|11! 12! 13!|

|12! 13! 14!|

a

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

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

^{2}a^{2}