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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}.[1 0 1] [c-b c+a a-b]

[1 1 0] [b-c a-c a+b]

show that ABA

^{-1 }is a diagonal matrix .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, show that the determinant :

1/a a

^{2}bc1/b b

^{2}ac = 01/c c

^{2}ab^{3}- b^{3}-c^{3}| x+a b c|

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

| c. a x+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

If elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero....

So can it b applied for ANY row or column???? Can v take any row of column of our choice or just the adjacent ones??? Such as 1st row with 3rd row and like 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 -abDifference between cramer's rule and Matrix method.....and when to use which one.....

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

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) .-1010-4040If det [ p b c

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

a b r]

determinant {5

^{2}5^{3}5^{4}5

^{3}5^{4}5^{5}5

^{4}5^{5}5^{6}}find the value of determinantPROVE 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????????

| 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

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)

prove without expanding that the determinant equals 0

b2c2 bc b-c

c2a2 ca c-a

a2b2 ab a-b

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

py+z y z

0 px+y py+z

= 0

where p is any real number

| 1 b b²-ca |

| 1 c c²-ab |

solve determinant with using properties

|b+c a a |

| b c+a b |=4abc

| c c a+b |

|2 y 3|

|1 1 z|

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

Find value of A(adjA)

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

[0 10]

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.

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 !!

^{T}|=16. The find the value of |2A|.^{PLEASE PROVIDE AN ANSWER WITHOUT LINKS }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}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|265 240 219

240 225 198

219 198 181

=0

Given I

_{2}. Find determinant I_{2}. also find determinant 3I_{2}.Evaluate the following determinants:

bar of (log

_{a}b 1)(1 log

_{b}a)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|.

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

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

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

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

A = [ 2 -3

3 4 ]

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

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}|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.

how to solve determinant of 4x4 matrix?

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

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.

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)

Following is the pictorial description for a particular page, selected by school administration. The total area of the page is 150 cm2 .The combined width of the margin at the top and bottom is 3 cm and the side 2 cm.

Using the information given above, answer the following: [PLS ANSWER ALL 5 QUESTIONS BELOW BECAUSE THEY ARE PART OF A SINGLE QUESTION] (with steps)

(i) The relation between x and y is given by

(a) (x-3) y = 150

(b) xy = 150

(c) x (y-2) = 150

(d) (x-2)(y-3) = 150

(ii) The area of page where printing can be done, is given by

(a) xy

(b) (x+3) (y+2)

(c) (x-3) ( y -2)

(d) (x-3) (y+2)

(iii) The area of the printable region of the page, in terms of x is

(a) 156 + 2x + 450/x

(b) 156 – 2x + 3(150/x)

(c) 156 – 2x – 15 (3/x)

(d) 156 – 2x – 3(150/x)

(iv) For what value of ‘x’, the printable area of the page is maximum?

(a) 15 cm

(b) 10 cm

(c) 12 cm

(d) 15 cm

(v) What should be the dimensions of the page so that it has maximum area to be printed?

(a) Length = 1 cm, width = 15 cm

(b) Length = 15 cm, width = 10 cm

(c) Length = 15 cm, width = 12 cm

(d) Length = 150 cm, width = 1cm

prove that determinant of x x

^{2 }yzy y

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

^{2}xysolve the following equation:

15-2x 11 10

11-3x 17 16 = 0

7-x 14 13

(a

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

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

^{2}+ a^{2})/bthe value of the det. of a matrix A of order 3x3 is 4. find the value of of |5A|

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|

prove that a+b+2c a b

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

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

A is a non singular matrices of order 4 and det(AdjA)=216. find det A

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

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}2ab b^{2}b

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

^{2}a^{2}