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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?

Q. 16. Find the value of ${a}_{23}+a{}_{32}$ in the matrix

A = ${\left[{a}_{ij}\right]}_{3x3}where{a}_{ij}=\left\{\begin{array}{l}\left|2i-j\right|ifij\\ -i+2j+3ifij\end{array}\right.$

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

show tha a

skew symmetric matrixofodd orderhas determinant=0write a square matrix of order 2 which is both symmetric and skew symmetric?

A = cosX sinX

-sinX cosX

then prove that

A

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

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?

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

find the number of 2*2 matrix satisfying...

i) a

_{ij }is 1 or -1ii) (a

_{11})^{2 }+(a_{12})^{2}= (a_{21})^{2}+ (a_{22})^{2}=2iii) a

_{11}a_{21}+ a_{12}a_{22}=0Two 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?

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

-5 1

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

3 0 -1

2 3 0

0 4 1

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

prove that the diagonal elements of a scew symmetric matrix are all zero

Use 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.

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

1 -1 0

find the inverse using elementary transformation

[4 3 3]

[-1 0 -1]

[-4 -4 -3]

and use it to solve the equations x-y = 3 , 2x +3y +4z = 17 , y + 2z = 7

[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.

A 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.

[ 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

Q. Find a matrix P satisfying the matrix equation $\left[\begin{array}{cc}2& 1\\ 3& 2\end{array}\right]P\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 2& -1\end{array}\right]$

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 matrix A= ( 1 2 3 ), write AA', where A' is the transpose of matrix A.

how is the value of 'n' calculated and why are the quantities squared and cubed ?

if A is a square matrix such that, A

^{2}=A, then write the value of (1+A)^{2}-3A.solve the following equation by matrix method: x-y+z=4, 2x+y-3z=0 x+y+z=2

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).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

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]

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

Q. If f (x) = ${x}^{2}-5x+7andA=\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$, find f (A).

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 :(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 + I$\mathbf{6}\mathbf{.}\mathbf{}IfthematrixA=\left[\begin{array}{ccc}5& 2& x\\ y& z& -3\\ 4& t& -7\end{array}\right]isasymmetricmatrix,findx,y,zandt.$

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).

_{11}= a_{12}=a_{13}=1, a_{21}= 0 , a_{22}= 1, a_{23}= 1 ,a_{31}=0, a_{32}= 0 , a_{33}= 1 , then use the principle of mathematical induction to show thatA

^{n}is equal to a_{11}= 1, a_{12}= n , a_{13}= n(n+1)/2 , a_{21}= 0 , a_{22}=1, a_{23}=n, a_{31}=0, a_{32}=0 , a_{33}=1 for every positive integers n .if A and B are symmetric matrices, then ABA is

a-symmetric

b-skew-symmetric

c-diagonal

d-scalar

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

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 ?

Three schools A, B and C organized a mela for collecting funds for helping the

rehabilitation of flood victims. They sold hand made fans, mats and plates from

recycled material at a cost of ` 25, ` 100 and ` 50 each. The number of articles sold

are given below :

Article A B C

hand fans4025 35

mats5040 50

plates20 30 40

~Find the funds collected by each school separately by selling the above articles. Also

find the total funds collected for the purpose.

Write one value generated by the above situation.

if A is any square matrix then prove that

AA

^{T }is symmetric?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.

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...:)

[-1 2 ] then show that A

^{2}+ 4A +7I = 0. Using this result find A^{3}Construct a 2x2 matrix A[aij] whose elements are given by

aij = { i - j , if i = j

i + j , if i

Thanks

Raagini

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

on A such that AB = AC implies B = C.