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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.
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 a2 bc
1/b b2 ac = 0
1/c c2 ab
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
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
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
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) .
{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
If 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
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
prove without expanding that the determinant equals 0b2c2 bc b-cc2a2 ca c-aa2b2 ab a-b
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
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
An amount of Rs. 50,000 is put into three investments at the rate of 6%,7% and 8% per annum respectively. The total annual income is Rs. 3,580. If the combined annual income from the first two investments is Rs. 700 more than the income from the third.
i) Represent the above situation by matrix equation and form linear equations using matrix multiplication.
ii) Is it possiblt to solve the system of equations so obtaines using matrices.
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
=0..
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
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)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 ?
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
WITHOUT EXPANDING the determinant at ANY stage, prove that :
x-3 x-4 x-A
x-2 x-3 x-B = 0
x-1 x-2 x-C
Where A,B,C are in Arithmatic progression.
easy way to solve elementary row or column transformation
A is a non singular matrices of order 4 and det(AdjA)=216. find det A
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|
Using the properties of determinants, prove that:
1 x x3
1 y y3 =(x-y) (y-z) (z-x) (x+y+z)
1 z z3
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
1 bc bc(b+c)
1 ca ca(c+a) = 0
1 ab ab(a+b)
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.
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)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|
rn|logb q 1| =0r
| log c r 1|
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 |
prove that a+b+2c a b c b+c+2a b = 2( a+b+c)3 c a c+a+2b
IF POINTS ( 2,0 ) ( 0, 5) AND ( X, Y ) ARE COLLINEAR THEN SHOW THAT X/2 + Y/5 = 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
Using determinants prove the following points are collinear..
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|
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!!!!!!
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)
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.
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 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 a2 bc
1/b b2 ac = 0
1/c c2 ab
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
| x+a b c|
| b. x+c. a|. =. 0 is -(a+b+c).
| c. a x+b|
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
A matrix of order 3X3 has determinant 5. What is the value of |3A|?
a2 2ab b2
b 2 a2 2ab = (a3+b3)2
2ab b 2 a2
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) .
{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
If det [ p b c
a q c = 0 then find (p/p-a) + (q/q-b) + (r/r-c)
a b r]
a2 1 a =
a a2 1 (a3-1)2
PROVE THAT THE DETERMINANT
b2+c2 ab ac
ab c2 +a2 bc
ac bc a2+b2
is equal to 4a2b2c2
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
prove without expanding that the determinant equals 0
b2c2 bc b-c
c2a2 ca c-a
a2b2 ab a-b
| 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
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
An amount of Rs. 50,000 is put into three investments at the rate of 6%,7% and 8% per annum respectively. The total annual income is Rs. 3,580. If the combined annual income from the first two investments is Rs. 700 more than the income from the third.
i) Represent the above situation by matrix equation and form linear equations using matrix multiplication.
ii) Is it possiblt to solve the system of equations so obtaines using matrices.
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 |
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
=0..
Difference between cramer's rule and Matrix method.....and when to use which one.....
(a2+ b2)/c c c
a (b2+ c2)/a a = 4abc
b b ( c2 + a2)/b
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
a2 2ab b2
b2 a2 2ab
2ab b2 a2
= (a3 + b3)2
|x p q|
|p x q| =(x-p)(x^2+px-2q^2)
|q q x|
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|.
A = [ 2 -3
3 4 ]
satisfies the equation x^2 - 6x + 17 = 0. Hence find A^-1.
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?
|x1 y1 2 |^2
|x2 y2 2| = 3a^4
|x3 y3 2|
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
Pls. answer
WITHOUT EXPANDING the determinant at ANY stage, prove that :
x-3 x-4 x-A
x-2 x-3 x-B = 0
x-1 x-2 x-C
Where A,B,C are in Arithmatic progression.
easy way to solve elementary row or column transformation
A is a non singular matrices of order 4 and det(AdjA)=216. find det A
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|
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)
Using the properties of determinants, prove that:
1 x x3
1 y y3 =(x-y) (y-z) (z-x) (x+y+z)
1 z z3
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
Using the properties of determinants, prove that:
1 bc bc(b+c)
1 ca ca(c+a) = 0
1 ab ab(a+b)
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.
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)2
Evaluate the following determinants:
bar of (log ab 1)
(1 logba)
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|
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 |
prove that a+b+2c a b
c b+c+2a b = 2( a+b+c)3
c a c+a+2b
IF POINTS ( 2,0 ) ( 0, 5) AND ( X, Y ) ARE COLLINEAR THEN SHOW THAT X/2 + Y/5 = 1
OR
Using properties of determinants, prove the following :
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..
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|
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!!!!!!
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)