मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

If A = [1-253],B=[1-34-7], then find the matrix A – 2B + 6I, where I is the unit matrix of order 2. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]`, then find the matrix A – 2B + 6I, where I is the unit matrix of order 2.

बेरीज

उत्तर

A – 2B + 6I = `[(1, -2),(5, 3)] - 2[(1, -3),(4, -7)] + 6[(1, 0),(0, 1)]`

= `[(1, -2),(5, 3)] - [(2, -6),(8, -14)] + [(6, 0),(0, 6)]`

= `[(1 - 2 + 6, -2 + 6 + 0),(5 - 8 + 0, 3 + 14 + 6)]`

= `[(5, 4),(-3, 23)]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Determinants and Matrices - Exercise 4.5 [पृष्ठ ८७]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 4 Determinants and Matrices
Exercise 4.5 | Q 2 | पृष्ठ ८७

संबंधित प्रश्‍न

Find the values of x and y if

`2 [(x,5),(7,y-3)] [(3,-4),(1,2)] = [(7,6),(15,14)]`


If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`

Verify that |AB| = |A|.|B|


If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.


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

verify that A (adj A) = (adj A) A = |A| . I


If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2),(0, 3)] "and C" = [(4, 3),(-1, 4),(-2, 1)]`, Show that A + B = B + A


If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]` , then find the matrix A − 2B + 6I, where I is the unit matrix of order 2.


If A = `[(1, -2),(3, -5),(-6, 0)],"B" = [(-1, -2),(4, 2),(1, 5)] "and C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.


If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, find (AT)T.


For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric, or neither.

`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`


For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`


Construct the matrix A = [aij]3×3 where aij = i − j. State whether A is symmetric or skew-symmetric.


Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]`  and X – 3Y = `[(0, -1),(0, -1)]`.


Find matrices A and B, if 2A – B = `[(6, -6, 0),(-4, 2, 1)]` and A – 2B = `[(3, 2, 8),(-2, 1, -7)]`.


Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] [(-1,  6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`.


If `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.


Find AT,  if A = `[(1, 3),(-4, 5)]`


If A = `[(5, -3),(4, -3),(-2, 1)]`, prove that (AT)T = A.


If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find AT + 4BT.


If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find 5AT – 5BT.


Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(1, 2, 4),(3, 2, 1),(-2, -3, 2)]`


Express each of the following matrix as the sum of a symmetric and a skew symmetric matrix `[(4, -2),(3, -5)]`.


If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.


Choose the correct alternative.

The matrix `[(0, 0, 0),(0, 0, 0)]` is _______


Fill in the blank :

If A = `[(4, x),(6, 3)]` is a singular matrix, then x is _______


Find matrices A and B, if `2"A" - "B" = [(6, -6, 0),(-4, 2, 1)] and "A" - 2"B" = [(3, 2, 8),(-2, 1, -7)]` 


If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.


Answer the following question:

Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`


Answer the following question:

If A = `[(1, -1, 0),(2, 3, 4),(0, 1, 2)]`, B = `[(2, 2, -4),(-4, 2, -4),(2, -1, 5)]`, show that BA = 6I


Choose the correct alternative:

If A = `[(1, 3/5, x),(y, -5, -7),(-4, -7, 0)]` is a symmetric matrix, then the values of x and y are ______ respectively.


Choose the correct alternative:

If A and B are two square matrices of order 3, then (AB)T = ______


State whether the following statement is True or False:

Every square matrix of order n can be expressed as sum of symmetric and skew symmetric matrix


State whether the following statement is True or False:

`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]` is a skew symmetric matrix


Find k, if A = `[(3, -2),(4, -2)]` and A2 = kA – 2I, where I is identity matrix of order 2


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×