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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' / .

|2 y 3|

|1 1 z|

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

Find value of A(adjA)

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 |

| x+a b c|

| b. x+c. a|. =. 0 is -(a+b+c).

| c. a x+b|

^{3}- b^{3}-c^{3}Without expanding, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}abIf 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 ]

Using the properties of determinants, prove that:

1 bc bc(b+c)

1 ca ca(c+a) = 0

1 ab ab(a+b)

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

without expanding the determinant show that-

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 -ab5.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

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

^{2}a

^{2}1 a =a a

^{2 }1 (a^{3}-1)^{2}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) .Solve this :$2.\mathrm{If}{\mathrm{D}}_{1}=\left|\begin{array}{ccc}{\mathrm{ab}}^{2}-{\mathrm{ac}}^{2}& {\mathrm{bc}}^{2}{\mathrm{a}}^{2}\mathrm{b}& {\mathrm{a}}^{2}\mathrm{c}-{\mathrm{b}}^{2}\mathrm{c}\\ \mathrm{ac}-\mathrm{ab}& \mathrm{ab}-\mathrm{bc}& \mathrm{bc}-\mathrm{ac}\\ \mathrm{c}-\mathrm{b}& \mathrm{a}-\mathrm{c}& \mathrm{b}-\mathrm{a}\end{array}\right|{\mathrm{D}}_{2}=\left|\begin{array}{ccc}1& 1& 1\\ \mathrm{a}& \mathrm{b}& \mathrm{c}\\ \mathrm{bc}& \mathrm{ac}& \mathrm{ab}\end{array}\right|,\mathrm{then}{\mathrm{D}}_{1}{\mathrm{D}}_{2}\mathrm{is}\mathrm{equal}\mathrm{to}-\phantom{\rule{0ex}{0ex}}\left(\mathrm{a}\right)0\left(\mathrm{b}\right){\mathrm{D}}_{1}^{2}\left(\mathrm{c}\right){\mathrm{D}}_{2}^{2}\left(\mathrm{d}\right){\mathrm{D}}_{2}^{3}$

If det [ p b c

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

a b r]

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

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}in properties of determinants how do we apply c1-c1+c2+c3 or ri-r1+r2+r3 in any row or column plz xplain wid an example

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

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

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

| 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

{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

py+z y z

0 px+y py+z

= 0

where p is any real number

dsing properties of determinant prove that :- determinant [ (mC1 mC2 mC3) , (nC1 nC2 nC3),(pC1 pC2 pC3)]= {mpn(m-n)(n-p)(p-m)}/12. determinant is of order 3*3 .

|b+c a a |

| b c+a b |=4abc

| c c a+b |

_{i}= [a^{i}b^{i}and |a|<1 ,|b| <1 then show that sigma i=1 to infinity |A_{i}|= a^{2}-b^{2}/(1-a^{2})(1-b^{2})b

^{i}a^{i}]Difference between cramer's rule and Matrix method.....and when to use which one.....

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

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

[0 10]

Ms. Priyanka Kediaor anyone else please do not redirect me to this page:

https://www.meritnation.com/ ask-answer/question/a- is -a -square -matrix -of -order -3 -and -det -a -7- write-t/determinants/6456894

This is not the same answer that I require. I just want a direct answer.

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 !!

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]

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

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|.

Evaluate the following determinants:

bar of (log

_{a}b 1)(1 log

_{b}a)What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ?

Using the properties of determinants ,show that

0 p-q p-r

q-p 0 q-r

r-p r-q 0

=0..

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

using the properties of determinants show that..

sin2x cos2x 1

cos2x sin2x 1

-10 12 2

=0..

(sin2x and cos2x means sin square x and cos square x respectively)

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}|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 .....)

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)

Without expanding the determinants show that

1 w w2

w w2 1

w2 1 w

=0 where w is one of the cube roots of unity.

(w2 means w square )

a

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

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

^{2}a^{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.

(a

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

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

^{2}+ a^{2})/bDeterminants cube root of unity question: Evaluate:| 1 w

^{3 }w^{5}||w

^{3 }1 w^{4}||w

^{5}w^{5}1 |, where w is an imaginary cube root of unity.

(I know the answer is 0 but how do you solve this determinant?)

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|

Using determinants prove the following points are collinear..

prove that a+b+2c a b

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

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

Using the properties of determinants ,show that..

2 3 7

13 17 5

15 20 12

=0..

without expanding the dterminant show that

1/a a2 bc

1/b b2 ca

1/c c2 ab

=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

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!!!!!!

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

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

^{2}1+z^{3}