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
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
Wherever possible, write the following as a single matrix.
`[(2, 3, 4),(5, 6, 7)] - [(0, 2, 3),(6, -1, 0)]`
Find x and y from the given equations:
`[(-8, x)] + [(y, -2)] = [(-3, 2)]`
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 = B – 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 . C + B . C
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
(A – B)2 = A2 – 2A . B + B2
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.
Classify the following matrix :
`|(800),(521)|`
Find the values of a and b) if [2a + 3b a - b] = [19 2].
If A = `|(1,9,4),(5 , 0 , 3)|` find A'
Evaluate the following :
`|(2,1) ,(3,2),(1 , 1)| |(1 , -2 , 1),(2 , 1 , 3)|`
Evaluate the following :
`|(0 , 1),(-1 , 2),(-2 , 0)| |(0 , -4 , 0),(3 , 0 , -1)|`
Evaluate the following :
`|(0 , 1 , 0),(2 , 0 , -3),(1 , 0 , -2)| |(1 , -2),(3 , 4),(0 , 0)|`
If A = `|(1,3),(3,2)|` and B = `|(-2 , 3),(-4 , 1)|` find BA
If P = `|(1 , 2),(2 , 1)|` and Q = `|(2 , 1),(1 , 2)|` find P (QP).
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) ?
Find the inverse of the matrix `[ (1, 2, 3), (1, 1, 5), (2, 4, 7)]` by using the adjoint method.
`
Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) `∃x cc` R such that x + 3 ≥ 10.
If `"A" = [(1,2,-3),(5,4,0)] , "B" = [(1,4,3),(-2,5,0)]`, then find 2A + 3B.
If A = `[(1,1),(2,2)] , "B" = [(1,2),(3,4)]` then find |AB|.
[2 3 – 7]
`[(3),(0),(-1)]`
`[(2 , 7, 8),(-1 , sqrt(2), 0)]`
Construct a 2 x 2 matrix whose elements aij are given by aij = 2i – j
Construct a 2 x 2 matrix whose elements aij are given by aij = i.j
Suppose determinant of a matrix Δ = 0, then the solution
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.
