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State whether the following is True or False : Singleton matrix is only row matrix. - Mathematics and Statistics

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प्रश्न

State whether the following is True or False :

Singleton matrix is only row matrix.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

Singleton matrix is also column matrix False.

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पाठ 2: Matrices - Miscellaneous Exercise 2 [पृष्ठ ८३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 2 Matrices
Miscellaneous Exercise 2 | Q 3.08 | पृष्ठ ८३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the matrix of the co-factor for the following matrix.

`[(1,3),(4,-1)]`


Find the inverse of the following matrix.

`[(1,2),(2,-1)]`


Find the inverse of the following matrix.

`[(2,0,-1),(5,1,0),(0,1,3)]`


Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.


Find the inverse of the following matrix (if they exist):

`((2,1),(1,-1))`


Find the inverse of the following matrix (if they exist):

`[(2,1),(7,4)]`


Find the inverse of the following matrix (if they exist):

`[(3,-10),(2,-7)]`


If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.


Choose the correct alternative.

If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______


Fill in the blank :

If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`


State whether the following is True or False :

If A and B are conformable for the product AB, then (AB)T = ATBT.


Solve the following :

If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.


A = `[(cos alpha, - sin alpha,  0),(sin alpha, cos alpha,  0),(0, 0, 1)]`, then A−1 is


If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33.


If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`


If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).


If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method


Choose the correct alternative:

If A is a non singular matrix of order 3, then |adj (A)| =  ______


If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.


If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)


If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.


If A and B non-singular matrix then, which of the following is incorrect?


If A is an invertible matrix of order 2 then det (A-1) be equal


If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.


Solve by using matrix inversion method:

x - y + z = 2, 2x - y = 0, 2y - z = 1


If A = `[(1,2),(3,-5)]`, then A-1 = ?


The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.


If A2 - A + I = 0, then A-1 = ______.


If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.


Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.


If A = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.


If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B–1 A–1)–1 is equal to ______.


If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`

Find (AB)–1 by adjoint method.

Solution:

AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`

AB = [  ]

|AB| =  `square`

M11 = –2  ∴ A11 = (–1)1+1 . (–2) = –2

M12 = –3     A12 = (–1)1+2 . (–3) = 3

M21 = 4       A21 = (–1)2+1 . (4) = –4

M22 = 3       A22 = (–1)2+2 . (3) = 3

Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`

adj (A) = [  ]

A–1 = `1/|A| . adj(A)`

A–1 = `square`


if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.


If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0


If A = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.


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