Home
Class 12
MATHS
In a certain city there are 30 colleges....

In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

Text Solution

AI Generated Solution

To solve the problem step by step, we will express the information given in the question as a column matrix and then use scalar multiplication to find the total number of posts of each kind in all the colleges. ### Step 1: Define the column matrix for one college We need to represent the number of each type of staff in one college as a column matrix. The number of staff in one college is: - Peons: 15 - Clerks: 6 ...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

A finance company has offices located in every division, every district and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superintendent, two clerks, one typist and one peon. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendent Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix notation find The total number of posts of each kind in all the offices taken together,

A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of each kind of office

A finance company has offices located in ewery division, every didtrict and every taluka in a certain state in India. Assume that there are five divisions, thirty districts and 200 talukas in the state. Each office has one head clerk, one cashier, one clerk and one peon. A divisional office has, in addition, one office superntendent, two clerks, one typist and one poen. A district office, has in addition, one clerk and one peon. The basic monthly salaries are as follows : Office superintendernt Rs 500, Head clerk Rs 200, cashier Rs 175, clerks and typist Rs 150 and peon Rs 100. Using matrix motation find the total basic monthly salary bill of all the offices taken together.

A particular resistance wire has a resistance of 3.0 ohm per metre. Find : The total resistance of three lengths of this wire each 1.5 m long, joined in parallel.

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 Rank of the matrix [(1,1,1),(1,-1,-1),(3,1,1)] is :

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 Rank of the matrix [(1,1,1,-1),(1,2,4,4),(3,4,5,2)] is :

Elementary Transformation of a matrix: The following operation on a matrix are called elementary operations (transformations) 1. The interchange of any two rows (or columns) 2. The multiplication of the elements of any row (or column) by any nonzero number 3. The addition to the elements of any row (or column) the corresponding elements of any other row (or column) multiplied by any number Echelon Form of matrix : A matrix A is said to be in echelon form if (i) every row of A which has all its elements 0, occurs below row, which has a non-zero elements (ii) the first non-zero element in each non –zero row is 1. (iii) The number of zeros before the first non zero elements in a row is less than the number of such zeros in the next now. [ A row of a matrix is said to be a zero row if all its elements are zero] Note: Rank of a matrix does not change by application of any elementary operations For example [(1,1,3),(0,1,2),(0,0,0)],[(1,1,3,6),(0,1,2,2),(0,0,0,0)] are echelon forms The number of non-zero rows in the echelon form of a matrix is defined as its RANK. For example we can reduce the matrix A=[(1,2,3),(2,4,7),(3,6,10)] into echelon form using following elementary row transformation. (i) R_2 to R_2 -2R_1 and R_3 to R_3 -3R_1 [(1,2,3),(0,0,1),(0,0,1)] (ii) R_2 to R_2 -2R_1 [(1,2,3),(0,0,1),(0,0,0)] This is the echelon form of matrix A Number of nonzero rows in the echelon form =2 rArr Rank of the matrix A is 2 The echelon form of the matrix [(1,3,4,3),(3,9,12,9),(1,3,4,1)] is :

Two mirros are inclinded by an angle 30^(@) . An object is placed 10^(@) with the mirror M_(1) . Find the positons of first two images formed by each mirror. Find the total number of images using (i) direct formula and (ii) counting the images.

An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question, a candidate earns 3 marks for choosing the correct opion, and -1 for choosing a wrong option. Assume that a candidate answers all questions by choosing exactly one option for each. Then find the number of distinct combinations of anwers which can earn the candidate a score from the set {15, 16,17,18, 19, 20}.

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. [[ x-y,2x+z] , [ 2x-y,3z+w ]] = [[ -1, 5 ] , [ 0, 13 ]], then ,x,y...

    Text Solution

    |

  2. Find the values of x , y , za n da which satisfy the matrix equation [...

    Text Solution

    |

  3. In a certain city there are 30 colleges. Each college has 15 peons, 6 ...

    Text Solution

    |

  4. If A=[(1,-1) ,(2 ,3)],B=[(2, 1), (1, 0)],p rove t h a t (A+B)^2!=A^2+...

    Text Solution

    |

  5. Find a matrix X such that 2A+B+X=0 , where A= [(-1, 2) ,(3, 4)],B=[(3,...

    Text Solution

    |

  6. If X and Y are 2xx2 matrices, then solve the following matrix equat...

    Text Solution

    |

  7. If A=[(alpha,0), (1, 1)]a n d B=[(1, 0), (5, 1)], find the values of a...

    Text Solution

    |

  8. Find the value of x such that [(1,x,1)][(1, 3, 2),( 2, 5, 1), (15, 3, ...

    Text Solution

    |

  9. If A=[(1,-1), (2,-1)],B=[(a,1),(b,-1)]a n d(A+B)^2=A^2+B^2,fin daa n d...

    Text Solution

    |

  10. If A=[[0,1],[-1,0]], find x\ a n d \ y such that (x I+y A)^2=A

    Text Solution

    |

  11. If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)], find A.

    Text Solution

    |

  12. Questions of matrix polynomial Equation

    Text Solution

    |

  13. If Aa n dB are symmetric matrices of the same order, write whether AB-...

    Text Solution

    |

  14. If A is a square matrix such that A^2=A ,t h e n(I+A)^3-7A is equal ...

    Text Solution

    |

  15. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  16. Construct a 3xx4 matrix A=[a(i j)] whose elements are given by (i)a...

    Text Solution

    |

  17. If [x-y2x+z2x-y3z+w]=[-1 5 0 13] , find x ,\ y ,\ z ,\ wdot

    Text Solution

    |

  18. Find dy/dx if x+y =( tanx)^2

    Text Solution

    |

  19. A matrix has 12 elements. What are the possible orders it can have?

    Text Solution

    |

  20. Find dy/dx If y= (sinx)^cosx .

    Text Solution

    |