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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?

What is cube root of unity i.e. omega???

show tha a

skew symmetric matrixofodd orderhas determinant=0if A is a square matrix of order 3 such that |Adj A| = 256. Find |2A'|.

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

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

^{ 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.Use matrix method, to find the rate of interest. Do you think people should donateto such trusts?

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

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

A = cosX sinX

-sinX cosX

then prove that

A

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

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?

(1) 5

(2) 4

(3) 3

(4) -4

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

3 0 -1

2 3 0

0 4 1

^{-1}= adjA /10, THEN FIND |3A|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

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.

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

if A=diag[2,-5,9], B=diag[-3,7,14] and c= diag[4,-6,3] find 2A+B-C

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.

[ 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

Q. The length of the latusrectum of a parabola is 4a . A pair of perpendicular tangents are drawn to the parabola to meet the axis of the parabola at the points A, B. If S is the focus of the parabola then $\frac{1}{\left|SA\right|}+\frac{{\displaystyle 1}}{{\displaystyle \left|SB\right|}}=$

A) 2/a

B) 4/a

C) 1/a

D) 2a

if A is a square matrix such that, A

^{2}=A, then write the value of (1+A)^{2}-3A.Area of the trapezium whose vertices lie on the parabola y

^{2}= 4x and its diagonals pass through (1, 0) and having length $\frac{25}{4}$ unit each, isA) $\frac{75}{4}$ sq. unit B) $\frac{625}{16}$ sq. unit C) $\frac{25}{4}$ sq. unit D) $\frac{25}{8}$ sq. unit

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

(i) If x and y represents the length and breadth of the rectangular tank, then the relation between the variables in terms of volume is

a) y = 4/x

b) x = 4/y

c) 2(xy+2y+2x)=8

d) xy +2y+2x = 8

(ii) The area of the 4 walls of the rectangular tank in terms of x and y is

a)4x+2y

b) 4x+4y

c)2x+4y

d)2x+2y

(iii) The total cost of buiding the tank is

a)Rs ( 40x+40y)

b) Rs (80x+80y)

c) Rs (120x+120y)

d)Rs (180x+180y)

(iv) The manufacturer of the tank is interested in minimizing the expense of the tank during construction. For this to happen the valve of x should be

a) 3 m

b) 5 m

c) 2 m

d) 8 m

(v) The minimum cost of construction of the tank is

a)Rs 2000

b) Rs 3000

c) Rs 1000

d) No minimum cost

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).A=IA for rows

and

A=AI for column?

using elementary row operations find the inverse of the matrix

0 1 2

1 2 3

3 1 1

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

-1 3 0

0 -2 1

Find the inverse of this matrix using elementary row operations and no links. pls provide the answer with the exact given values as i want to check my answer

URGENT:Find matrices A and B, if

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

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]

i m nt able to get anytng of ths concept plzz hepl :(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

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

how is it possible that A = A/2 + A/2 + A'/2 - A'/2??????

prove that

a

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

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

^{2 +}a^{2 }= 4abcThe Transpose of matrix of a 2*2 is clear .... But finding it difficult to find 3*3 ..... Help US

If A is a square matrix such that A

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

^{3 }= 7A + Ihow to find inverse of a matrix.i'm facing a lot of problem in it!

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).

........................... = ............ ............................ = ............

tan 5 A + tan 3 A sin 8A cot A . cot 4 A - 1 cos 5 A

3) cot 6 A - tan 2 A cos 8 A

......................... = ............

cot 6 A + tan 2 A cos 4 A

if A and B are symmetric matrices, then ABA is

a-symmetric

b-skew-symmetric

c-diagonal

d-scalar

^{-1}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

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 ?

if A is any square matrix then prove that

AA

^{T }is symmetric?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?using concept of inverseA [ 1 2 ] = [ 1 -1 ]

3 4 0 0

2 3

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...:)

Q. If $\left|\begin{array}{cc}x& x\\ 1& x\end{array}\right|=\left|\begin{array}{cc}3& 2\\ 1& 2\end{array}\right|$. Find the value of x.

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 .

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.