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Syllabus

A school wants to award its student for the values of honesty,regularity and hard work with a total cash award of RS. 6000.Three times the award money for hardwork added to that given for honesty amounts to RS 11000.The award money given for honesty and hard work together is double the one given for regularity.Represent the above situation algebraically and find the award money for each value,using matrix method.apart from these values ,namely, honesty, regularity and hardwork, suggest one more value which the school must include for awards?

19.A company is to employ 60 labourers from either of the party X or Y, comprising in age groups as under : Rate of labour applicable to categories I, II and III are Rs. 1200, Rs. 1000 and Rs. 600 respectively. Using matrix multiplication, find which party is economically preferable.What is cube root of unity i.e. omega???

Q. If A = $\left(\begin{array}{ccc}0& -1& 2\\ 2& -2& 0\end{array}\right)$ and B =$\left(\begin{array}{cc}0& 1\\ 1& 0\\ 1& 1\end{array}\right)$, find a matrix C such that CAB = I = ABC, where I is the 2 x 2 unit matrix.

show tha a

skew symmetric matrixofodd orderhas determinant=0sinx cosx ( in sq. brackets)

write a square matrix of order 2 which is both symmetric and skew symmetric?

Q.5. If A be a square matrix of the order 5 and B = Adj (A) then find Adj (5A).

find the number of all possible matrices of order 2*3 with each entry 0 or 1

For keeping fit X people believe in morning walk, Y people believe in yoga Z ppl join gym. Total no. of people are 70. Further 20% 30% 40% ppl are suffering from any disease who believe in morning walk,yoga gym. Total no of such ppl is 21. If morning walk costs Rs.0, yoga Rs500 per month gym Rs400 total expenditure is Rs23000. Formulate a matrix problem calculate the no of each type of ppl.

^{ 1}/_{2}% respectively. The total annual interest from these three accounts is 550 RUPEES. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts using matrix method._{ij}]is a square matrix such that a_{ij}= i-j, then determine whether A is symmetric or skew symmetric .Use matrix method, to find the rate of interest. Do you think people should donateto such trusts?

If A = (aij) is a 2 x 3 matrix and aij = i+j, write down the matrix completely.

the number of possible matrices of order 3x3 with each entry 0 or 1 is: (A)27 (B)18 (C)81 (D)512 andhow?

if A B are symmetric C is a skew symmetric matrix, then ABC -CBA is alwys-?

Two schools A and B decided to award prices to their students for 3 values, honesty(X),punctuality(Y), andobedience(Z). School A decided to award a total of Rs.11000 for the three values to 5,4,and 3 students while school B decided to award Rs.10,700 for the 3 values to be 4,3,5 2students . If all the 3 prices together amount to be Rs. 2700, then:

1. Represent the abuve situation by a matric waequation and form linear equations using matrix multiplication.

2. Is it possible to solve the system of equations so obtained using matrices?

3. Which value do you nprefer to be rewarded and why?

(a) r = min(m,n)

(b) r>min(m,n)

(c) r less than equal to min(m,n)

(d) none of these

1) Using elementary transformations, find the inverse of the matrix

3 0 -1

2 3 0

0 4 1

A=[COS2X SIN2X]

[-SIN2X COS 2X]

IT IS A matrix... find A

^{2}prove that the diagonal elements of a scew symmetric matrix are all zero

^{2}-5x+ 6 .. find f(A) if A= matrix 2 0 12 1 3

1 -1 0

for square matricsA &B of order n, define 'o' as follow : AoB = 1/2(AB +BA)

SHOW THAT

1) AoB = BoA

2) AoI

_{n}= A3) AoA = A

^{2}4)Ao(B+C) =AoB+AoC

find the inverse using elementary transformation

[4 3 3]

[-1 0 -1]

[-4 -4 -3]

[2 1] A [-3 2] = [ 1 0]

3 2 5 -3 0 1

Two schools P and Q want to award their selsected students on the values of Discipline, Politeness and Punctuality. The school P wants to award Rs. x each, Rs.y each and Rs.z each for the three respective values to its 3,2 and 1 students with a total amount money of Rs.1000/- School Q wants to spent Rs.1500/- to award its 4, 1 and 3 students on the respective values. If the total amount of awards for one prize on each value is Rs.600/-, using matrices, find the award money for each value.

Q.Shefali has made these marks monthwise to count the number of days to her birthday. On which date did she stare the tally marks ? On which date is her birthday ?Hint ;First count the numbers in the middle to find which month it is.)[ cos

^{2}θ cosθsinθ ][cosθsinθ sin

^{2}θ ]and

[ cos

^{2}α cosαsinα ][cosαsin α sin

^{2}α ]is zero when and differ by an odd multiples of pi/ 2

If li,mi,ni where i=1,m=2,n=3 denote the direction cosines of 3 mutually perpendicular vectors in space ,prove that AA^T=I wher A is a matrix and A^T is its transpose and I is a indentity matrix

if A is a square matrix such that, A

^{2}=A, then write the value of (1+A)^{2}-3A.Two Trusts A and B receive Rs 70000 and 55000 respectively from central government to award prize to persons of a district in three fields of agriculture, education, and social service .Trust A awarded 10, 5,and 15 persons in the field of agriculture, education and social service respectively while trust B awarded 15,10,and 5 persons respectively. If all three prizes together amount to 6000, then find the amount of each prize by matrix method ?

if B, C ARE n ROWED SQUARE MATRICES AND IF A=B+C , BC=CB ,C

^{2}=0 ,THEN SHOW THAT FOR EVERY n is the element ofN, A^{n+1}=B^{n}(B+(n+1)C).Q.21. Find the value of $\theta in\left[0,2\mathrm{\pi}\right]$ such that the matrix $\left[\begin{array}{ccc}2\mathrm{sin}\theta -1& \mathrm{sin}\theta & \mathrm{cos}\theta \\ \mathrm{sin}\left(\theta +\pi \right)& 2\mathrm{cos}\theta -\sqrt{3}& \mathrm{tan}\theta \\ \mathrm{cos}\left(\mathrm{\theta}-\mathrm{\pi}\right)& \mathrm{tan}\left(\mathrm{\pi}-\mathrm{\theta}\right)& 0\end{array}\right]$ is a skew symmetric matrix.

using elementary row operations find the inverse of the matrix

0 1 2

1 2 3

3 1 1

2a+b=4 and a-2b=-3

if matrix cos2pi/7 -sin2pi/7

sin2pi/7 cos 2pi/7 the whole power k = matrix 1 0

0 1 , then write the value of x+y+xy

URGENT:Find matrices A and B, if

2A - B = and 2B + A = .

if for a matrix A , A to the power 5 = I , THEN A inverse =

let A=[2 3 AND F(X)= X

^{2}-4X+7. SHOW THAT F(A) =O. USE THIS RESULT TO FIND A^{5}.-1 2]

a line can be drawn which divides the following figure into two separate pare. These two parts is could then fit together to make a square, which two numbers would you connect to make this line

an amount of 600 crores is spent by the government in 3 schemes. scheme A is for saving girl child from the cruel parents who donot want girl childand get abortion before her birth. scheme B is fror saving of newly wed girls from death due to dowry. scheme c is planning for good healt for senior citizens. now twice the amount spent on scheme B together with amount spent on A is rs 700 crores. and three time the amount spent on scheme A together with amount spnt on Scheme B and Scheme C is rs1200 crores. find the amount spent on each scheme using matrices.

Prove that the product of matrix [cos

^{2}~~0~~cos~~0~~sin~~0~~(below dis)cos~~0~~sin~~0~~sin^{2}~~0~~] & [cos^{2}alpha cosalphasinalpha (below dis)cosalphasinalpha sin^{2}~~0~~] is a null matrix where~~0~~& alpha diffre by an odd multiple of pie / 2.i m nt able to get anytng of ths concept plzz hepl :(Thank you

if AB r 2 matrices AB=B BA=A then A^2+B^2=

prove that

a

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

^{2}+c^{2}/a ab b c

^{2 +}a^{2 }= 4abcIf A is a square matrix such that A

^{2 }= A. Show that :-(I + A)

^{3 }= 7A + IA is a square matrix of order n. l=maximum number of distinct enteries if A is a triangular matrix. m=maximum number of distinct enteries if A is a diagonal matrix. p=minimum number of zeroes if A is a triangular matrix. if l+5=p+2m , find the order of the matrix.

find the value of X and Y..if 2X+3Y=[ 2 3 , 4 0 ] (2x2 matrix) and 3X+2Y=[ 2 -2 , -1 5 ] (2x2 matrix).

3 4] 2 1] 20 13] apply R2 -> R2- R1 and then apply C2=C2-C1

if A and B are symmetric matrices, then ABA is

a-symmetric

b-skew-symmetric

c-diagonal

d-scalar

1. Using matrix method, solve the following system of equations :

2/x + 3/y + 10/z = 4, 4/x - 6/y + 5/z = 1, 6/x + 9/y - 20/z = 2

2. For what value of x, the matrix [5-x x+1

2 4 ] is singular?

Give an example of two non-zero 2x2 matrix A and B. such that AB=0

how many marks is dis fr d xam ???

there are two families M and N . there are 2 men , 2 women, and 4 childern in family N . and 4 men , 6 women and 2 children in family M . there commended daily allowance for calories is child : 1800, women : 1900 and man : 2400 and for protiens is man :55gm, woman : 45gm and child :33gm. using matrices algebra, calculate the total requirement of protiens and calories for each of the famlies ?

x+y ka hole square=

if A is any square matrix then prove that

AA

^{T }is symmetric?help me to find the answer I couldn't get the correct answer

Q.find the inerse of the matrix using elimentary row transformation

Ten students were selected from a school on the basis of values for giving awards and were divided into three groups. The first group comprises hard workers,the second group has honest and law abiding students and the third group consists vigilant and obedient students. Double the number of students of the first group added to the number in the second group gives 13, while the combined strength of first and second group is 4 times that of the third group. Find the number of students in each group.

AandBwant to award their selected teachers on the values ofhonesty, hard workandregularity. The school A wants to awardRsxeach,Rsyeach andRszeach for the three respective values to3, 2and1 teacherswith a total award money ofRs1.28lakhs. School B wants to spendRs1.54lakhsto award its4, 1and3 teacherson the respective values(by giving the same award money for the three values as before). If the total amount of award for one prize on each value isRs57000, using matrices, find the award money for each value?There are two families A and B. There are 2 men 3 women and 1 child in the family A and 1 man 1 woman and 2 children are there in family B. The recommended daily allowance of calories is men 2400, women 1900, and children 1800. Represent the above data in matrix form...

Here how can we put into matrix form and please post answer with explaination... Please experts...:)

Construct a 2x2 matrix A[aij] whose elements are given by

aij = { i - j , if i = j

i + j , if i

Thanks

Raagini

For what value of k, the matrix( 2-k ) 3 is not invertible.

-5 1

Articles school. x. Y Z

Hand-held fans. 30. 40. 35

Mats. 12. 15. 20

Toys. 70. 55. 75

using matrices , find the funds collected by each school by selling the above articles and the total funds collected . Also write any one value generated by the above situations .

A = cosX sinX

-sinX cosX

then prove that

A

^{n}= cos nX sin nX-sin nX cos nX , n belongs to all natural no.

If the matrix

Ais both symmetric and skew symmetric, thenA.Ais a diagonal matrixB.Ais a zero matrixC.Ais a square matrixD.None of theseUse matrix multiplication to divide rs. 30,000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts rs. 3060.

If A, B, C are three non zero square matrices of same order, find the condition

on A such that AB = AC implies B = C.Q. Express the matrix A = $\left[\begin{array}{cc}3& 5\\ 1& -1\end{array}\right]$ as the sum of a symmetric and a skew symmetric matrix.