Advertisements
Advertisements
Question
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 1/2 |-3i + j|`
Solution
In general, a 3 × 4 matrix is given by `A = [(a_11, a_12,a_13,a_14), (a_21,a_22, a_23, a_24), (a_31,a_32, a_33, a_34)]`
`a_(ij) = 1/2 |-3i + j|, i = 1,2,3 and j = 1,2 ,3,4`
`:. a_11 = 1/2 |-3xx1+1| = 1/2|-3+1| = 1/2|-2| = 2/2=1`
`a_12 = 1/2|-3xx1+2|= 1/2|-3+2| = 1/2|-1|= 1/2`
`a_13 = 1/2|-3xx1+3|=1/2|-3+3| = 0`
`a_14 = 1/2 |-3xx1+4| = 1/2|-3+4| = 1/2|1| = 1/2`
`a_21 = 1/2|-3xx2+1|=1/2|-6+1|=1/2|-5|=5/2`
`a_22 = 1/2|-3xx2+2|=1/2|-6+2| = 1/2|-4| = 4/2 = 2`
`a_23 = 1/2|-3xx2+3|=1/2|-6+3| = 1/2|-3| = 3/2`
`a_24 = 1/2|-3xx2+4|= 1/2 |-6+4 = 1/2|-2| = 2/2 = 1|`
`a_31 = 1/2|-3xx3+1|=1/2|-9+1|=1/2|-8|=8/2 = 4`
`a_32 = 1/2|-3xx3+2| = 1/2|-9+2| = 1/2|-7|=7/2`
`a_33 = 1/2 |-3xx3+3|=1/2|-9+3|=1/2|-6|=6/2 = 3`
`a_34 = 1/2 |-3xx3+4| = 1/2 |-9+4| = 1/2|-5| = 5/2`
Therefore, the required matrix is A = `[(1, 1/2, 0, 1/2), (5/2, 2, 3/2, 1), (4, 7/2, 3,5/2)]`
APPEARS IN
RELATED QUESTIONS
Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.
If A is a 3 × 3 matrix |3A| = k|A|, then write the value of k.
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
Write the number of elements,
In the matrix A = `[(2,5,19,-7),(35,-2, 5/2 ,12), (sqrt3, 1, -5 , 17)]`
Write the elements a13, a21, a33, a24, a23
Construct a 2 × 2 matrix, `A = [a_(ij)]` whose elements are given by `a_(ij) = (1 + 2j)^2/2`
Construct a 3 × 4 matrix, whose elements are given by `a_(ij) = 2i - j`
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is ______.
If A, B are symmetric matrices of same order, then AB − BA is a ______.
Find matrix A such that `((2,-1),(1,0),(-3,4))A = ((-1, -8),(1, -2),(9,22))`
Find the value of k if M = `[(1,2),(2,3)]` and `M^2 - km - I_2 = 0`
The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
If a matrix has 5 elements, write all possible orders it can have.
Construct a matrix A = [aij]2×2 whose elements aij are given by aij = e2ix sin jx.
If A = `[(2, 3),(1, 2)]`, B = `[(1, 3, 2),(4, 3, 1)]`, C = `[(1),(2)]`, D = `[(4, 6, 8),(5, 7, 9)]`, then which of the sums A + B, B + C, C + D and B + D is defined?
If `[(2x, 3)] [(1, 2),(-3, 0)] [(x),(8)]` = 0, find the valof x.
Construct a2 × 2 matrix where aij = `("i" - 2"j")^2/2`
Construct a2 × 2 matrix where aij = |–2i + 3j|
Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is ______.
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is ______.
The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is ____________.
The number of all the possible matrices of order 2 x 2 with each entry 0, 1, or 2 is ____________.
The order of [x y z] `[("a","h","g"),("h","b","f"),("g","f","c")] [("x"),("y"),("z")]` is ____________.
`[(2,0,3),(5,1,0),(0,1,-1)]`
The order of the single matrix obtained from `[(1,-1),(0,2),(2,3)] {[(-1,0,2),(2,0,1)] - [(0,1,23),(1,0,21)]}` is ____________.
If A is a matrix of order m x n and B is a matrix such that AB’ and B'A are both defined, then the order of matrix B is ____________.
If A is an m x n matrix such that AB and BA are both defined, then B is a ____________.
Given that matrices A and B are of order 3 × n and m × 5 respectively, then the order of matrix C = 5A + 3B is:
The order of set A is 3 and that of set B is 2. What is the number of relations from A to B?
Consider the following information regarding the number of men and women workers in three factories I, II and III
| MEN WORKERS | WOMEN WORKERS | |
| I | 30 | 25 |
| II | 25 | 31 |
| III | 27 | 26 |
Which of the following represent the above information in the form of a 3 × 2 matrix.
The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AAT is 9, is equal to ______.
Let P = `[(1, 0, 0),(3, 1, 0),(9, 3, 1)]` and Q = [qij] be two 3 × 3 martices such that Q – P5 = I3. Then `(q_21 + q_31)/q_32` is equal to ______.
If A is a 2 × 3 matrix such that AB and AB' both are defined, then the order of the matrix B is ______.
