Advertisements
Advertisements
प्रश्न
If A = `[(4, 2),(-1, x)]` and such that (A – 2I)(A – 3I) = 0, find the value of x
उत्तर
A = `[(4, 2),(-1, x)]`
A – 2I = `[(4, 2),(-1, x)] - 2[(1, 0),(0, 1)]`
= `[(4, 2),(-1, x)] - [(2, 0),(0, 2)]`
= `[(4 - 2, 2 - 0),(-1 - 0, x - 2)]`
A – 2I = `[(2, 2),(-1, x - 2)]`
A – 3I = `[(4, 2),(-1, x)] - 3[(1, 0),(0, 1)]`
= `[(4, 2),(-1, x)] - 3[(3, 0),(0, 3)]`
= `[(4 - 3, 2 - 0),(-1 - 0, x - 3)]`
A – 3I = `[(1, 2),(-1, x - 3)]`
(A – 2I)(A – 3I) = `[(2, 2),(-1, x 2)] [(1, 2),(-1, x - 3)]`
= `[(2 -2, 4 + 2(x - 3)),(-1 - (x - 2), -2 + (x - 2)(x - 3))]`
= `[(0, 4 + 2x- 6),(-1 - x + 2, -2 + x^2 - 3x - 2x + 6)]`
(A – 2I)(A – 3I) = `[(0, 2x - 2), (-x + 1, x^2 - 5x + 4)]`
Given (A – 2I)(A – 3I) = 0
∴ `[(0, 2x - 2), (-x + 1, x^2 - 5x + 4)] = [(0, 0),(0, 0)]`
Equation the corresponding entries
2x – 2 = 0
⇒ x = 1
x2 – 5x + 4 = 0 ......(1)
Put x = 1 in equation (1)
12 – 5 × 1 + 4 = 5 – 5 = 0
∴ The reqired value of x is x = 1
APPEARS IN
संबंधित प्रश्न
In the matrix A = `[(8, 9, 4, 3),(- 1, sqrt(7), sqrt(3)/2, 5),(1, 4, 3, 0),(6, 8, -11, 1)]`, write The number of elements
If A = `[(5, 2, 2),(-sqrt(17), 0.7, 5/2),(8, 3, 1)]` then verify (AT)T = A
If A is of order p × q and B is of order q × r what is the order of AB and BA?
For the given matrix A = `[(1, 3, 5, 7),(2, 4, 6, 8),(9, 11, 13, 15)]` the order of the matrix AT is
If A = `[(1, 2, 3),(3, 2, 1)]`, B = `[(1, 0),(2, -1),(0, 2)]` and C = `[(0, 1),(-2, 5)]` Which of the following statements are correct?
(i) AB + C = `[(5, 5),(5, 5)]`
(ii) BC = `[(0, 1),(2, -3),(-4, 10)]`
(iii) BA + C = `[(2, 5),(3, 0)]`
(iv) (AB)C = `[(-8, 20),(-8, 13)]`
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Construct an m × n matrix A = [aij], where aij is given by
aij = `|3"i" - 4"j"|/4` with m = 3, n = 4
If A = `[(1, "a"),(0, 1)]`, then compute A4
If A = `[(1, 0, 2), (0, 2, 1), (2, 0, 3)]` and A3 – 6A2 + 7A + kI = 0, find the value of k
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 and BA ≠ 0
Show that f(x) f(y) = f(x + y), where f(x) = `[(cosx, -sinx, 0),(sinx, cosx, 0),(0, 0, 1)]`
Verify the property A(B + C) = AB + AC, when the matrices A, B, and C are given by A = `[(2, 0, -3),(1, 4, 5)]`, B = `[(3, 1),(-1, 0),(4, 2)]` and C = `[(4, 7),(2, 1),(1,-1)]`
Find the matrix A which satisfies the matrix relation `"A"= [(1, 2, 3),(4, 5, 6)] = [(-7, -8, -9),(2, 4, 6)]`
If AT = `[(4, 5),(-1, 0),(2, 3)]` and B = `[(2, -1, 1),(7, 5, -2)]`, veriy the following
(A + B)T = AT + BT = BT + AT
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
If A = `[(1, 2, 2),(2, 1, -2),(x, 2, y)]` is a matrix such that AAT = 9I, find the values of x and y
Choose the correct alternative:
If a ≠ b, b, c satisfy `|("a", 2"b", 2"c"),(3, "b", "c"),(4, "a", "b")|` = 0, then abc =
Let det M denotes the determinant of the matrix M. Let A and B be 3 × 3 matrices with det A = 3 and det B = 4. Then the det (2AB) is
A matrix is an ordered:-
Let (p1, q1, r1) and (p2, q2, r2) are satisfying `|(1, p, p^2),(1, q, q^2),(1, r, r^2)|` = 6 (where pi, qi ri ∈ N and pi < qi < ri and i = 1, 2) and point (p1, q1, r1) lies on the plane 2x + 3y + 6z = k, and point (p2, q2, r2) lies on the plane 2x + 3y + 6z = k2 (where p1 = p2 = 1) If distance between these planes is 'd', then value of (210d) is ______.
