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 – 3j - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

aij = i – 3j

बेरीज

उत्तर

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

aij = i – 3j

∴ a11 = 1 – 3(1) = 1 – 3 = –2,

a12 = 1 – 3(2) = 1 – 6 = –5,

a21 = 2 – 3(1) = 2 – 3 = –1,

a22 = 2 – 3(2) = 2 – 6 = – 4

a31 = 3 – 3(1) = 3 – 3 = 0,

a32 = 3 – 3(2) = 3 – 6 = –3

∴ A = `[(-2, -5),(-1, -4),(0, -3)]`

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] 11 Standard Maharashtra State Board
पाठ 4 Determinants and Matrices
Exercise 4.4 | Q 1. (ii) | पृष्ठ ८२

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.


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

If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.


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.


Solve for a, b and c; if `[(a, a - b),(b + c, 0)] = [(3, -1),(2, 0)]`


Evaluate:     

`2[(-1      0)/(2 -3)]  +[(3      3)/(5    0)]`


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

A2 – B2 = (A + B) (A – B)


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


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


Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.  


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) |`


Find the values of x and y, if  `|(3"x" - "y"),(5)| = |(7) , ("x + y")|`


Find the values of a, b, c and d, if `|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`


If P= (8,5),(7,2) find : P + Pt


If A = `|(5,"r"),("p",7)|` , c and if A + B = (9,7),(5,8) , find the values of p,q,r and s.


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)|`


If P =`|(1 , 2),(3 , 4)|` , Q = `|(5 , 1),(7 , 4)|` and R = `|(2 , 1),(4 , 2)|`  find the value of  P(Q + R)


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) ?


If A = `[(2, 3), (1, 2)], B = [(1, 0),(3, 1)]`, Find (AB)-1


If A = `[(1,2), (1,3)]`, find A2 - 3A


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.


Find the adjoint of the matrix `"A" = [(2,-3),(3,5)]`


If A = `[(1,1),(2,2)] , "B" = [(1,2),(3,4)]` then find |AB|.


Using the truth table statement, examine whether the statement pattern (p → q) ↔ (∼ p v q) is a tautology, a contradiction or a contingency.


`[(2, -1),(5, 1)]`


`[(3),(0),(-1)]`


`[(0, 0, 0),(0, 0, 0)]`


Construct a 2 x 2 matrix whose elements aij are given by aij = 2i – j


I2 is the matrix ____________.


If A is a matrix of order m × 3, B is a matrix of order 3 × 2 and R is a matrix of order 5 × n such that AB = R, the value of m and n are ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×