हिंदी

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. - Mathematics

Advertisements
Advertisements

प्रश्न

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.

योग

उत्तर

Number of different types of posts in any college is given by

`X = [[15],[6],[1],[1]]`

Total number of posts of each kind in all the colleges = 30X

`=30[[15],[6],[1],[1]]`

`=30[[450],[180],[30],[30]]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Algebra of Matrices - Exercise 5.2 [पृष्ठ १९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 5 Algebra of Matrices
Exercise 5.2 | Q 21 | पृष्ठ १९

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


if `A = [(0, -tan  alpha/2), (tan  alpha/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I -A)[(cos alpha, -sin alpha),(sin alpha, cos alpha)]`


if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`


if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer


If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N


If A is a square matrix such that A2 = A, then (I + A)3 – 7 A is equal to ______.


A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?


If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.


If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(0, 4, 7),(-4, 0, -3),(-7, 3, 0)]`


Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`


If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.


If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2


Select the correct option from the given alternatives:

Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______


Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A


Answer the following question:

If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.


Answer the following question:

If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix


Choose the correct alternative:

If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______


Choose the correct alternative:

If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______


State whether the following statement is True or False:

If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1


State whether the following statement is True or False:

If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2 


If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______


The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.


AB = AC ⇒ B = C for any three matrices of same order.


If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.


The matrix A `=[(0,1),(1,0)]` is a ____________.


If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.


If a matrix A is both symmetric and skew symmetric then matrix A is ____________.


`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?


Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0


If the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.


The minimum number of zeros in an upper triangular matrix will be ______.


If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×