English

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 - Mathematics

Advertisements
Advertisements

Question

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

Advertisements

Solution

It is given that  A = `[(0,1),(0,0)]`

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise 3.5 [Page 100]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 3 Matrices
Exercise 3.5 | Q 1 | Page 100

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


Find the value of x, y, and z from the following equation:

`[(4,3),(x,5)] = [(y,z),(1,5)]`


Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`


Given two matrices A and B 

`A = [(1,-2,3),(1,4,1),(1,-3, 2)]  and B  = [(11,-5,-14),(-1, -1,2),(-7,1,6)]`

find AB and use this result to solve the following system of equations:

x - 2y + 3z = 6, x + 4x + z = 12, x - 3y + 2z = 1


If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.


Investigate for what values of λ and μ the equations
2x + 3y + 5z = 9
7x + 3y - 2z = 8
2x + 3y + λz = μ have
A. No solutions
B. Unique solutions
C. An infinite number of solutions.


If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| . 


Choose the correct alternative.

The matrix `[(8, 0, 0),(0, 8, 0),(0, 0, 8)]` is _______


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, -2, 4),(0, 0, -5),(0, 0, 0)]`


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)]`


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?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`


Find k if the following matrix is singular:

`[(7, 3),(-2, "k")]`


Find k if the following matrix is singular:

`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`


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


Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

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


If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A2 – 4A is a scalar matrix 


State whether the following statement is True or False:

If A is non singular, then |A| = 0


State whether the following statement is True or False:

If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2 


If A = `[(3, 1),(-1, 2)]`, then prove that A2 – 5A + 7I = O, where I is unit matrix of order 2


A square matrix A = [aij]nxn is called a diagonal matrix if aij = 0 for ____________.


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 ____________.


The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.


If a matrix A is both symmetric and skew symmetric then matrix A is ____________.


A matrix is said to be a row matrix, if it has


A square matrix B = [bÿ] m × m is said to be a diagonal matrix if all diagonal elements are


If all the elements are zero, then matrix is said to be


A = `[a_(ij)]_(m xx n)` is a square matrix, if


Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0


How many matrices can be obtained by using one or more numbers from four given numbers?


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 A is a square matrix of order 3, then |2A| is equal to ______.


Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100

Reason: AB = BA implies AB = BA for all positive integers n.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×