Advertisements
Advertisements
प्रश्न
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:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Advertisements
उत्तर
Let A = `[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
∴ AT = `[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
∴ AT = A, i.e., A = AT
∴ A is a symmetric matrix.
APPEARS IN
संबंधित प्रश्न
If A is a square matrix, such that A2=A, then write the value of 7A−(I+A)3, where I is an identity matrix.
Find the value of x, y, and z from the following equation:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
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`
Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.
Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O
If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.
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)]`
If li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
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:
`[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`
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:
`[(5),(4),(-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:
`[(6, 0),(0, 6)]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
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 _______
State whether the following statement is True or False:
If A is non singular, then |A| = 0
State whether the following statement is True or False:
If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2
If A = `[(1, 3, 3),(3, 1, 3),(3, 3, 1)]`, then show that A2 – 5A is a scalar matrix
If A and B are matrices of same order, then (3A –2B)′ is equal to______.
AB = AC ⇒ B = C for any three matrices of same order.
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
The matrix A `=[(0,1),(1,0)]` is a ____________.
If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
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
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
If D = `[(0, aα^2, aβ^2),(bα + c, 0, aγ^2),(bβ + c, (bγ + c), 0)]` is a skew-symmetric matrix (where α, β, γ are distinct) and the value of `|((a + 1)^2, (1 - a), (2 - c)),((3 + c), (b + 2)^2, (b + 1)^2),((3 - b)^2, b^2, (c + 3))|` is λ then the value of |10λ| is ______.
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 is a square matrix of order 3, then |2A| is equal to ______.
Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100
Reason: AB = BA implies AB = BA for all positive integers n.
A matrix which is both symmetric and skew symmetric matrix is a ______.
