Advertisements
Advertisements
प्रश्न
Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.
Advertisements
उत्तर
Let A = `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]`
∴ A' = `[(0, y, 3/2),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
∴ –A' = `-[(0, y, 3/2),(-5"i", 0, -sqrt(2)),(x, z, 0)]`
= `[(0, -y, -3/2),(5"i", 0, sqrt(2)),(-x, -z, 0)]`
Since A is a skew-symmetric matrix, A = – A'
∴ `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)] = [(0, -y, -3/2),(5"i", 0, sqrt(2)),(-x, -z, 0)]`
∴ by equality of matrices, we get,
x = `-3/2, y = 5"i" and z = sqrt(2)`
APPEARS IN
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Find the value of x, y and z from the following equation:
`[(4, 3),(x, 5)] = [(y, z),(1, 5)]`
Find the value of x, y, and z from the following equation:
`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`
Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`
If A = `[(α, β),(γ, -α)]` is such that A2 = I, then ______.
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
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?
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:
`[9 sqrt(2) -3]`
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:
`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A
Answer the following question:
If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
Show by an example that for A ≠ O, B ≠ O, AB = O
If A is a square matrix, then A – A’ is a ____________.
If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.
`root(3)(4663) + 349` = ? ÷ 21.003
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
The minimum number of zeros in an upper triangular matrix will be ______.
Let A = `[(0, -2),(2, 0)]`. If M and N are two matrices given by M = `sum_(k = 1)^10 A^(2k)` and N = `sum_(k = 1)^10 A^(2k - 1)` then MN2 is ______.
If A = `[(0, -tan θ/2),(tan θ/2, 0)]` and (I2 + A) (I2 – A)–1 = `[(a, -b),(b, a)]` then 13(a2 + b2) is equal to ______.
If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.
If A is a square matrix of order 3, then |2A| is equal to ______.
What is the order of a column matrix with \[m\] rows?
What is the order of a row matrix with \[n\] columns?
Which elements form the diagonal of a square matrix?
Which elements can be non-zero in a diagonal matrix?
An identity matrix (unit matrix) is a square matrix with:
Which condition defines an identity matrix?
A zero matrix (null matrix) is a matrix in which:
