मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Construct a matrix A = = [aij]3×2 whose element aij is given by aij = (i-j)25-i - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Construct a matrix A = [aij]3 × 2 whose element aij is given by

aij = `(("i" - "j")^2)/(5 - "i")`

बेरीज
Advertisements

उत्तर

A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`

Given that aij = `(("i" - "j")^2)/(5 - "i")`

∴ a11 = `((1 - 1)^2)/(5 - 1) = 0/4` = 0

a12 = `((1 - 2)^2)/(5 - 1) = 1/4`

a21 = `((2 - 1)^2)/(5 - 2) = 1/3`

a22 = `((2 - 2)^2)/(5 - 2) = 0/3` = 0

a31 = `((3 - 1)^2)/(5 - 3) = 4/2` = 2

a32 = `((3 - 2)^2)/(5 - 3) = 1/2`

∴ A = `[(0, 1/4),(1/3, 0),(2, 1/2)]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants and Matrices - Exercise 4.4 [पृष्ठ ८२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 4 Determinants and Matrices
Exercise 4.4 | Q 1. (i) | पृष्ठ ८२

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

State, whether the following statement is true or false. If false, give a reason.

The matrices A2 × 3 and B2 × 3 are conformable for subtraction.


State, whether the following statement is true or false. If false, give a reason.

A column matrix has many columns and only one row.


Given : `[(x, y + 2),(3, z - 1)] = [(3, 1),(3, 2)]`; find x, y and z.


If A = `[(8, -3)]` and B = `[(4, -5)]`; find B – A


If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find B + C


If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – C


If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A + B – C


Wherever possible, write the following as a single matrix.

`[(1, 2),(3, 4)] + [(-1, -2),(1, -7)]`


Wherever possible, write the following as a single matrix.

`[(0, 1, 2),(4, 6, 7)] + [(3, 4),(6, 8)]`


Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find M + Mt


State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

A . (B – C) = A . B – A . C


If M = `[(2,1),(1,-2)] `; find M2, M3 and M5.


Find cofactors of the elements of the matrix A = `[(-1, 2),(-3, 4)]`.


Solve the following system of linear equation using matrix method: 
`1/x + 1/y +1/z = 9`

`2/x + 5/y+7/z = 52`

`2/x+1/y-1/z=0`


Classify the following rnatrix : 

`|(2,1),(0 , 6),(8 , 7) |`


Classify the following matrix :

`|(1 , 1),(0,9)|`


Find the values of a and b) if [2a + 3b a - b] = [19  2]. 


If M =`|(8,3),(9,7),(4,3)|` and N = `|(4,7),(5,3),(10,1)|` find M - N


If A = `|(1,9,4),(5 , 0 , 3)|`  find A'


If B = `|(15 , 13),(11,12),(10,17)|` , find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.


Evaluate the following :

`|(1 , 1),(2 , 3)|  |(2 , 1),(1 , 4)|`


Evaluate the following :

`|(2 , 3),(-4 , 0)| |(3 , -2),(-1 , 4)|`


Evaluate the following :

`|(2,1) ,(3,2),(1 , 1)|  |(1 , -2 , 1),(2 , 1 , 3)|` 


Evaluate the following :

`|(0 , 1 , 0),(2 , 0 , -3),(1 , 0 , -2)|  |(1 , -2),(3 , 4),(0 , 0)|`


Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B)  (ii) A2 - B2 . Is (i) equal to (ii) ?


Solve the equation x + y = 4 and 2x - y = 5 using the method of reduction.


Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.


`[(2 ,- 4),(0 ,0),(1 , 7)]`


If a matrix has 8 elements, what are the possible order it can have?


Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X


Construct a matrix A = [aij]3 × 2 whose element aij is given by

aij = i – 3j


Construct a matrix A = [aij]3 × 2 whose element aij is given by

aij = `(("i" + "j")^3)/5`


Suppose determinant of a matrix Δ = 0, then the solution


I2 is the matrix ____________.


A, B and C are three matrices each of order 5; the order of matrix CA + B2 is ______.


If a matrix A = `[(0, 1),(2, -1)]` and matrix B = `[(3),(1)]`, then which of the following is possible:


If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×