मराठी

Write the Number of All Possible Matrices of Order 2 × 2 with Each Entry 1, 2 Or 3. - Mathematics

Advertisements
Advertisements

प्रश्न

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

बेरीज

उत्तर

As matrices is of order 2 × 2, so there are 4 entries possible.

Each entry has 3 choices that are 1, 2 or 3

So, number of ways to make up such matrices are 3 × 3 × 3 × 3 i.e, 34 times or 81 times.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Algebra of Matrices - Exercise 5.6 [पृष्ठ ६५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 5 Algebra of Matrices
Exercise 5.6 | Q 65 | पृष्ठ ६५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Compute the indicated products:

`[[1     -2],[2     3]][[1         2        3],[-3    2      -1]]`


Compute the products AB and BA whichever exists in each of the following cases:

`A=[[3     2],[-1     0],[-1      1]]` and `B= [[4         5        6],[0           1             2]]`


If A = `[[2       -1],[3             2]]`  and B = `[[0         4],[-1          7]]`find 3A2 − 2B + I


If A = `[[ab,b^2],[-a^2,-ab]]` , show that A2 = O

 

If A = `[[ cos 2θ     sin 2θ],[ -sin 2θ    cos 2θ]]`, find A2.


 If `[[2     3],[5      7]] [[1      -3],[-2       4]]-[[-4      6],[-9        x]]` find x.


If\[A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}\] f (x) = x2 − 2x − 3, show that f (A) = 0


If A=then find λ, μ so that A2 = λA + μI

 

Find the matrix A such that    [2  1  3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`


`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.


`A=[[2,0,1],[2,1,3],[1,-1,0]]` , find A2 − 5A + 4I and hence find a matrix X such that A2 − 5A + 4I + = 0.

 

If `A=[[1,1],[0,1]] ,` Prove that `A=[[1,n],[0,1]]` for all positive integers n.


If A and B are square matrices of the same order, explain, why in general

(A + B)2 ≠ A2 + 2AB + B2


If A and B are square matrices of the same order, explain, why in general

(− B)2 ≠ A2 − 2AB + B2


Let `A=[[1,1,1],[3,3,3]],B=[[3,1],[5,2],[-2,4]]` and `C=[[4,2],[-3,5],[5,0]]`Verify that AB = AC though B ≠ CA ≠ O.

 

A trust fund has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of(ii) Rs 2000


To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

(i) ₹50       (ii) ₹20       (iii) ₹40

The number of attempts made in three villages XY and Z are given below:

          (i)               (ii)              (iii)
X      400              300             100
Y      300              250               75
Z      500              400             150

Find the total cost incurred by the organisation for three villages separately, using matrices.

 

A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.

 

Let  `A =[[2,-3],[-7,5]]` And `B=[[1,0],[2,-4]]` verify that 

 (A + B)T = AT BT


 If \[A = \begin{bmatrix}\sin \alpha & \cos \alpha \\ - \cos \alpha & \sin \alpha\end{bmatrix}\] , verify that AT A = I2.
 

If  \[A = \begin{bmatrix}\cos x & - \sin x \\ \sin x & \cos x\end{bmatrix}\]  , find AAT

 

If \[A = \begin{bmatrix}- 3 & 0 \\ 0 & - 3\end{bmatrix}\] , find A4.


If A = [aij] is a 2 × 2 matrix such that aij = i + 2j, write A.


If A is a matrix of order 3 × 4 and B is a matrix of order 4 × 3, find the order of the matrix of AB


If A is a square matrix such that A2 = A, then write the value of 7A − (I + A)3, where I is the identity matrix.


If A and B are two matrices such that AB = A and BA = B, then B2 is equal to


The matrix  \[A = \begin{bmatrix}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{bmatrix}\] is a


Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.


Prove by Mathematical Induction that (A′)n = (An)′, where n ∈ N for any square matrix A.


If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.


A matrix which is not a square matrix is called a ______ matrix.


Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as

School/Article DPS CVC KVS
Handmade/fans 40 25 35
Mats 50 40 50
Plates 20 30 40

Based on the information given above, answer the following questions:

  • What is the total amount of money collected by all three schools DPS, CVC, and KVS?

Three schools DPS, CVC, and KVS decided to organize a fair for collecting money for helping the flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each respectively. The numbers of articles sold are given as

School/Article DPS CVC KVS
Handmade/fans 40 25 35
Mats 50 40 50
Plates 20 30 40

Based on the information given above, answer the following questions:

  • How many articles (in total) are sold by three schools?

Let a, b, c ∈ R be all non-zero and satisfy a3 + b3 + c3 = 2. If the matrix A = `((a, b, c),(b, c, a),(c, a, b))` satisfies ATA = I, then a value of abc can be ______.


If A = `[(-3, -2, -4),(2, 1, 2),(2, 1, 3)]`, B = `[(1, 2, 0),(-2, -1, -2),(0, -1, 1)]` then find AB and use it to solve the following system of equations:

x – 2y = 3

2x – y – z = 2

–2y + z = 3


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×