Advertisements
Advertisements
Question
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
Options
1 + α² + βγ = 0
1 – α² + βγ = 0
1 – α² – βγ = 0
1 + α² – βγ = 0
Advertisements
Solution
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then 1 – α² – βγ = 0.
Explanation:
A = `[(alpha, beta), (ϒ, -alpha)]`
`"A"^2 = "A" * "A"[(alpha, beta), (ϒ, -alpha)][(alpha, beta), (ϒ, -alpha)]`
= `[(alpha^2 + betaϒ, alphabeta - alphabeta), (alphaϒ - alphaϒ, betaϒ + alpha^2)] = [(1, 0), (0, 1)]`
Now, A2 = I
⇒ `[(alpha^2 + betaϒ,0), (0, betaϒ + alpha^2)] = [(1, 0), (0, 1)]`
α2 + βγ = 1 or 1 – α2 – βγ = 0
Accordingly, option (1 - α2 - βγ = 0) is correct.
APPEARS IN
RELATED QUESTIONS
`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.
If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.
Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.
If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.
If A and B are square matrices of the same order 3, such that ∣A∣ = 2 and AB = 2I, write the value of ∣B∣.
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:
`[(6, 0),(0, 6)]`
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)]`
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)]`
If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.
If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.
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?
Answer the following question:
If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
Choose the correct alternative:
If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______
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______.
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","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.
If A is a square matrix, then A – A’ is a ____________.
If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.
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.
If a matrix A is both symmetric and skew-symmetric, then ____________.
The matrix A `=[(0,1),(1,0)]` is a ____________.
The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]` is a ____________.
`root(3)(4663) + 349` = ? ÷ 21.003
`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?
If all the elements are zero, then matrix is said to be
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
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 `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
A matrix which is both symmetric and skew symmetric matrix is a ______.
