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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' / .
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) .
for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?
[0 10]
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 ]
prove without expanding that the determinant equals 0b2c2 bc b-cc2a2 ca c-aa2b2 ab a-b
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
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
A matrix of order 3X3 has determinant 5. What is the value of |3A|?
{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
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)2
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
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, prove that:
1 x x3
1 y y3 =(x-y) (y-z) (z-x) (x+y+z)
1 z z3
Difference between cramer's rule and Matrix method.....and when to use which one.....
if A is a square matrix and det A = 2 , then write the value of det AA' where A' is the transpose of matrix A.
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
265 240 219
240 225 198
219 198 181
=0
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)
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 ?
IF POINTS ( 2,0 ) ( 0, 5) AND ( X, Y ) ARE COLLINEAR THEN SHOW THAT X/2 + Y/5 = 1
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?
Without expanding, show that the determinant :
1/a a2 bc
1/b b2 ac = 0
1/c c2 ab
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
Pls. answer
easy way to solve elementary row or column transformation
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|
let a be the square matrix of order 3*3.write the value of mod of 2A where mod of A = 4
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
=0..
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
determinant {52 53 54
53 54 55
54 55 56}find the value of determinant
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.
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|
prove that a+b+2c a b c b+c+2a b = 2( a+b+c)3 c a c+a+2b
solve the system of equationsx-y+2z=1
2y-3z=1
3x-2y+4z=2
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
Without expanding the determinants show that :
42 1 6
28 7 4
14 3 2
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|
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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' / .
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 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 .
for any 2*2 matrix A, if A(adjA) = [10 0] find A determinant....?
[0 10]
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 ]
prove without expanding that the determinant equals 0
b2c2 bc b-c
c2a2 ca c-a
a2b2 ab a-b
if a is a square matrix of order 3 and / 3A / = k/A/ find value of k? pls fast plss
|2 y 3|
|1 1 z|
xyz=80 and 3x+2y+10z=20
Find value of A(adjA)
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
y y2 1+y3 = 0 , then show that 1+xyz = 0 ?
z z2 1+z3
A matrix of order 3X3 has determinant 5. What is the value of |3A|?
{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
| b^2 +c^2 ab ac |
| ab c^2+a^2 bc |=4a^2b^2c^2
| ca cb a^2+ b^2|
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
Show that
[y+z x y]
[z+x z x]
[x+y y z]
=(x +y+z) (x-z)2
state any short tricks to solve prob. on properties of determinant. and identify how to solve it by slight seeing????????
|x p q|
|p x q| =(x-p)(x^2+px-2q^2)
|q q x|
|x1 y1 2 |^2
|x2 y2 2| = 3a^4
|x3 y3 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
A = [ 2 -3
3 4 ]
satisfies the equation x^2 - 6x + 17 = 0. Hence find A^-1.
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, prove that:
1 x x3
1 y y3 =(x-y) (y-z) (z-x) (x+y+z)
1 z z3
Difference between cramer's rule and Matrix method.....and when to use which one.....
if A is a square matrix and det A = 2 , then write the value of det AA' where A' is the transpose of matrix A.
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
a2 2ab b2
b 2 a2 2ab = (a3+b3)2
2ab b 2 a2
265 240 219
240 225 198
219 198 181
=0
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)
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 ?
IF POINTS ( 2,0 ) ( 0, 5) AND ( X, Y ) ARE COLLINEAR THEN SHOW THAT X/2 + Y/5 = 1
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?
Without expanding, show that the determinant :
1/a a2 bc
1/b b2 ac = 0
1/c c2 ab
Show that the elements along the main diagonal of a skew symmetric matrix are all zero.
Pls. answer
easy way to solve elementary row or column transformation
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.
prove that the 3x3 determinant :
| 1+a2-b2 2ab -2b |
| 2ab 1-a2+b2 2a | = (1+a2+b2)3
| 2b -2a 1-a2-b2 |
If , find A-1. Using A-1,
Solve the system of linear equations :
4x - 5y - 11z = 12, x - 3y + z = 1, 2x + 3y - 7z = 2.
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)
let a be the square matrix of order 3*3.write the value of mod of 2A where mod of A = 4
if A is a square matrix of order 3 such that adj(2A) = k adj(A) , then wite the value of k..
Using the properties of determinants ,show that
0 p-q p-r
q-p 0 q-r
r-p r-q 0
=0..
prove that determinant of x x2 yz
y y2 zx = (x-y)(y-z)(z-x)(xy+yz+zx)
z z2 xy
determinant {52 53 54
53 54 55
54 55 56}find the value of determinant
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.
no links please
(a2+ b2)/c c c
a (b2+ c2)/a a = 4abc
b b ( c2 + a2)/b
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,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
solve the system of equations
x-y+2z=1
2y-3z=1
3x-2y+4z=2
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
Without expanding the determinants show that :
42 1 6
28 7 4
14 3 2
=0
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!!!!!!