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Using properties of determinants prove that -
(b+c)2....a2........a2
b2.....(c+a)2......b2 =2abc(a+b+c)3
c2.....c2.......(a+b)2
In this ques.. i just want to know tht after applying C1→ C1-C2, C2→ C2-C3
in this ques how can i take (a+b+c) common from C1 and C2.
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' / .
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 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 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 b2 + bc c2 + bc
a2 + ac -ac c2 + ac
a2 + ab b2 + ab -ab
265 240 219
240 225 198
219 198 181
=0
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
PROVE THAT THE DETERMINANT
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
1. Using properties of determinants, prove the following:
| x y z
x2 y2 z2
x3 y3 z3 | = xyz(x - y)(y - z)(z - x) .
2. Using properties of determinants, prove the following :
| x x2 1+px3
y y2 1+py3
z z2 1+pz3 | = (1+ pxyz)(x - y)(y - z)(z - x) .
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
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
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)2
prove without expanding that the determinant equals 0b2c2 bc b-cc2a2 ca c-aa2b2 ab a-b
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 !!
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]
Using properties of determinats, prove that
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)2
What is the formula for Det[ adj( adj(A) ) ] and how do you derive it ?
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
Pls. answer
1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.
easy way to solve elementary row or column transformation
Without expanding the determinant , show that | 1 a a2 | | 1 bc b+c |
| 1 b b2 | = | 1 ca c+a |
| 1 c c2 | | 1 ab a+b |
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?
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.
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
how to solve determinant of 4x4 matrix?
If A is an invertible matrix of order 3 and |A|=5, then find |adj A|
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
If the value of the third order determinant be 11,then what is value of the square of determinant formed by its cofactor?
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|
rn|logb q 1| =0r
| 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
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)
if A is a square matrix of order 3 and det adjA=64 find detA and det A -1HELP NEEDED URGENT
| a^2+b^2/c c c |
| a b2+c2/a a |
|b b c2+a2/b|
prove that a+b+2c a b c b+c+2a b = 2( a+b+c)3 c a c+a+2b
Mr. X has invested a part of his investment in 10% bond A and a part in 15% bond B. His interest income during first year is Rs. 4000. If he invests 20% more in 10% bond A and 10% more in 15% bond B, his income during the second year increases by Rs. 500. Find his initial investment using matrix method
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!!!!!!
the r.d sharma 2007 editn. exercise. 6.2 pg. no.6.41, qwestn numb.1 pat no. 6 plz tell no hints available.............. :(((
for what value of x is the following matrix singular
[3-2x x+1
2 4 ]
E.g: 9876543210, 01112345678
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Syllabus
Using properties of determinants prove that -
(b+c)2....a2........a2
b2.....(c+a)2......b2 =2abc(a+b+c)3
c2.....c2.......(a+b)2
In this ques.. i just want to know tht after applying C1→ C1-C2, C2→ C2-C3
in this ques how can i take (a+b+c) common from C1 and C2.
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' / .
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 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 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|?
| b^2 +c^2 ab ac |
| ab c^2+a^2 bc |=4a^2b^2c^2
| ca cb a^2+ b^2|
Prove that the following determinant is equal to (ab + bc + ca)3 :
-bc b2 + bc c2 + bc
a2 + ac -ac c2 + ac
a2 + ab b2 + ab -ab
265 240 219
240 225 198
219 198 181
=0
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
PROVE THAT THE DETERMINANT
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
1. Using properties of determinants, prove the following:
| x y z
x2 y2 z2
x3 y3 z3 | = xyz(x - y)(y - z)(z - x) .
2. Using properties of determinants, prove the following :
| x x2 1+px3
y y2 1+py3
z z2 1+pz3 | = (1+ pxyz)(x - y)(y - z)(z - x) .
(a2+ b2)/c c c
a (b2+ c2)/a a = 4abc
b b ( c2 + a2)/b
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
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
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)2
py+z y z
0 px+y py+z
= 0
where p is any real number
sin^2A cotA 1
sin^2B cotB 1 =0
sin^2C cotC 1
prove without expanding that the determinant equals 0
b2c2 bc b-c
c2a2 ca c-a
a2b2 ab a-b
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 !!
Difference between cramer's rule and Matrix method.....and when to use which one.....
|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
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)2
|sin(A+B+C) sin B cos C |
|-sinb 0 tan A | = 0,if A+B+c=pi?
|cos(A+B) -tan A 0 |
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 ?
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
Pls. answer
1. A square matrix A, of order 3, has |A|=5, find |A adj. A|.
easy way to solve elementary row or column transformation
Without expanding the determinant , show that | 1 a a2 | | 1 bc b+c |
| 1 b b2 | = | 1 ca c+a |
| 1 c c2 | | 1 ab a+b |
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?
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.
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
A = [ 2 -3
3 4 ]
satisfies the equation x^2 - 6x + 17 = 0. Hence find A^-1.
how to solve determinant of 4x4 matrix?
If A is an invertible matrix of order 3 and |A|=5, then find |adj A|
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
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)
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
If the value of the third order determinant be 11,then what is value of the square of determinant formed by its cofactor?
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
|c b-x a|
|b a c-x|
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)
if A is a square matrix of order 3 and det adjA=64 find detA and det A -1HELP NEEDED URGENT
a2 2ab b2
b 2 a2 2ab = (a3+b3)2
2ab b 2 a2
| a^2+b^2/c c c |
| a b2+c2/a a |
|b b c2+a2/b|
prove that a+b+2c a b
c b+c+2a b = 2( a+b+c)3
c a c+a+2b
Mr. X has invested a part of his investment in 10% bond A and a part in 15% bond B. His interest income during first year is Rs. 4000. If he invests 20% more in 10% bond A and 10% more in 15% bond B, his income during the second year increases by Rs. 500. Find his initial investment using matrix method
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!!!!!!
the r.d sharma 2007 editn. exercise. 6.2 pg. no.6.41, qwestn numb.1 pat no. 6 plz tell no hints available.............. :(((
for what value of x is the following matrix singular
[3-2x x+1
2 4 ]