English

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: [6006] - Mathematics and Statistics

Advertisements
Advertisements

Question

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)]`

Sum

Solution

Since all the non-diagonal elements are zero and diagonal elements are same, it is a scalar matrix.

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Determinants and Matrices - Exercise 4.4 [Page 83]

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

If A is a square matrix, such that A2=A, then write the value of 7A(I+A)3, where I is an identity matrix.


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

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


if `A = [(0, -tan  alpha/2), (tan  alpha/2, 0)]` and I is the identity matrix of order 2, show that I + A = `(I -A)[(cos alpha, -sin alpha),(sin alpha, cos alpha)]`


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`


if `A = [(3,-4),(1,-1)]` then prove A"=` [(1+2n, -4n),(n, 1-2n)]` where n is any positive integer


If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.


Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O


Using coding matrix A=`[(2,1),(3,1)]` encode the message THE CROW FLIES AT MIDNIGHT.


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


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:

`[(0, 4, 7),(-4, 0, -3),(-7, 3, 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:

`[(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)]`


Find k if the following matrix is singular:

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


If A = `[(5, 1, -1),(3, 2, 0)]`, Find (AT)T.


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.


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


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


If A = `[(2, 0, 0),(0, 1, 0),(0, 0, 1)]`, then |adj (A)| = ______


If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______


If two matrices A and B are of the same order, then 2A + B = B + 2A.


If A is a square matrix, then A – A’ is a ____________.


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


If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.


A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an


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


A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.


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


If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.


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×