Advertisements
Advertisements
प्रश्न
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 _______
पर्याय
λ = 0
λ2 – 3λ – 4 = 0
λ2 + 3λ – 4 = 0
λ2 – 3λ – 6 = 0
उत्तर
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then λ2 – 3λ – 4 = 0
Explanation:
Since A – λI is a singular matrix,
A – λI = 0
`[(1, 3),(2, 2)] - λ[(1, 0),(0, 1)] = 0 `
`[(1, 3),(2, 2)] - [(λ, 0),(0, λ)] = 0`
`[(1 - λ, 3),(2, 2 - λ)] = 0`
∴ (1 – λ) (2 – λ) – 6 = 0
∴ 2 − λ − 2λ + λ2 − 6 = 0
∴ 2 – 3λ + λ2 – 6 = 0
∴ λ2 – 3λ – 4 = 0
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:
`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`
Let A = `[(0,1),(0,0)]`show that (aI+bA)n = anI + nan-1 bA , where I is the identity matrix of order 2 and n ∈ N
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`
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
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?
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:
`[(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)]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Identify the following matrix is singular or non-singular?
`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`
Find k if the following matrix is singular:
`[(7, 3),(-2, "k")]`
Find k if the following matrix is singular:
`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`
Answer the following question:
If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C
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
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 = `[(3, 1),(-1, 2)]`, then prove that A2 – 5A + 7I = O, where I is unit matrix of order 2
The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.
AB = AC ⇒ B = C for any three matrices of same order.
Show by an example that for A ≠ O, B ≠ O, AB = O
If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.
If A is a square matrix, then A – A’ is a ____________.
For any square matrix A, AAT is a ____________.
If a matrix A is both symmetric and skew-symmetric, then ____________.
A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are
A diagonal matrix is said to be a scalar matrix if its diagonal elements are
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
A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.
The minimum number of zeros in an upper triangular matrix will be ______.
How many matrices can be obtained by using one or more numbers from four given numbers?
If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.
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 `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
If A is a square matrix of order 3, then |2A| is equal to ______.
