Advertisements
Advertisements
Question
Construct a 3 × 3 matrix whose elements are given by aij = `("i" + "j")^3/3`
Solution
a11 = `(1 + 1)^3/3 = 2^3/3 = 8/3`
a12 = `(1 + 2)^3/3 = 27/3` = 9
a13 = `(1 + 3)^3/3 = 64/3 = 64/3`
a21 = `(2 + 1)^3/3 = 27/3` = 9
a22 = `(2 + 2)^3/3 = 64/3 = 64/3`
a23 = `(2 + 3)^3/3 = 125/3 = 125/3`
a31 = `(3 + 1)^3/3 = 64/3 = 64/3`
a32 = `(3 + 2)^3/3 = 125/3 = 125/3`
a33 = `(3 + 3)^3/3 = 216/3` = 72
The required matrix A = `[(8/3, 9, 64/3),(9, 64/3, 125/3),(64/3, 125/3, 72)]`
APPEARS IN
RELATED QUESTIONS
If A = `[(5, 2, 2),(-sqrt(17), 0.7, 5/2),(8, 3, 1)]` then verify (AT)T = A
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
Transpose of a column matrix is
If A = `[(1, 0, 0),(0, 1, 0),("a", "b", - 1)]`, show that A2 is a unit matrix
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A + B)T = AT + BT = BT + AT
Choose the correct alternative:
If A = `[(1, 2, 2),(2, 1, -2),("a", 2, "b")]` is a matrix satisfying the equation AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to
Choose the correct alternative:
If A is a square matrix, then which of the following is not symmetric?
Choose the correct alternative:
Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?
Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det A = 3 and det B = 4. Then the det (2AB) is
A matrix is an ordered:-
