Advertisements
Advertisements
Question
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
Solution
`A + A^T=[(2 4),(3 5)] + [(2 3),(4 5)] = [(4 7),(7 10)]`
∴ `(A + A^T)^T = [(4 7),(7 10)]=(A + A^T)`
∴ A + AT is symmetric matrix.
APPEARS IN
RELATED QUESTIONS
Find the value of x, y, and z from the following equation:
`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`
if `A = [(0, -tan alpha/2), (tan alpha/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I -A)[(cos alpha, -sin alpha),(sin alpha, cos alpha)]`
if A = [(1,1,1),(1,1,1),(1,1,1)], Prove that A" = `[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]` `n in N`
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3
In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?
Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`
Choose the correct alternative.
The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Select the correct option from the given alternatives:
If A and B are square matrices of equal order, then which one is correct among the following?
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
Show by an example that for A ≠ O, B ≠ O, AB = O
Given A = `[(2, 4, 0),(3, 9, 6)]` and B = `[(1, 4),(2, 8),(1, 3)]` is (AB)′ = B′A′?
For any square matrix A, AAT is a ____________.
If a matrix A is both symmetric and skew-symmetric, then ____________.
The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
A matrix is said to be a row matrix, if it has
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
If all the elements are zero, then matrix is said to be
The number of all possible matrices of order 3/3, with each entry 0 or 1 is
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0
If A is a square matrix of order 3, then |2A| is equal to ______.