Advertisements
Advertisements
प्रश्न
Construct a matrix A = [aij]3 × 2 whose element aij is given by
aij = i – 3j
Advertisements
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)]`
APPEARS IN
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.
Transpose of a 2 × 1 matrix is a 2 × 1 matrix.
Solve for a, b and c; if `[(a, a - b),(b + c, 0)] = [(3, -1),(2, 0)]`
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.
`[(0, 1, 2),(4, 6, 7)] + [(3, 4),(6, 8)]`
Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix Mt. If possible, find Mt – M
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.
(B . C) . A = B . (C . A)
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
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 matrix :
`[(7, 0)]`
Classify the following matrix :
`|(800),(521)|`
Classify the following matrix :
`|(11 , 3 , 0),(21 , 8 , 4),(15,5,2)|`
Find the values of a and b) if [2a + 3b a - b] = [19 2].
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 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)|`
If A = `|(1,3),(3,2)|` and B = `|(-2 , 3),(-4 , 1)|` find BA
If A = `|(3,-2),(-1 , 4)|` , B = `|(2"a"),(1)|` , C = `|(-4),(5)|` , D = `|(2),("b")|` and AB + 2C = 4D then find the values of a and b.
Solve the equation 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 = `[(1,2,3), (2,k,2), (5,7,3)]` is a singular matrix then find the value of 'k'.
If `"A" = [(1,2,-3),(5,4,0)] , "B" = [(1,4,3),(-2,5,0)]`, then find 2A + 3B.
If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A-1 by using elementary transformation .
[2 3 – 7]
`[(2 , 7, 8),(-1 , sqrt(2), 0)]`
`[(0, 0, 0),(0, 0, 0)]`
Construct a 2 x 2 matrix whose elements aij are given by aij = i.j
Choose the correct answer from the given four options :
If A = [aij]2×2 where aij = i + j, then A is equal to
If A = `[(5, -2),(7, -0)]` and B = `[(8),(3)]`, then which of the following is not possible?
If a matrix A = `[(0, 1),(2, -1)]` and matrix B = `[(3),(1)]`, then which of the following is possible:
Event A: Order of matrix A is 3 × 5.
Event B: Order of matrix B is 5 × 3.
Event C: Order of matrix C is 3 × 3.
Product of which two matrices gives a square matrix.
