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: [3-2400-5000]

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:

`[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`

Sum
Advertisements

Solution

Let A = `[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`

Since all the elements below the diagonal are zero in matrix A., it is an upper triangular matrix.

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Determinants and Matrices - Exercise 4.4 [Page 82]

APPEARS IN

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.


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.


If for any 2 x 2 square matrix A, `A("adj"  "A") = [(8,0), (0,8)]`, then write the value of |A|


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


Find the matrix X so that X`[(1, 2, 3),(4, 5, 6)]= [(-7, -8, -9),(2, 4, 6)]`


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


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


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 li, mi, ni, i = 1, 2, 3 denote the direction cosines of three mutually perpendicular vectors in space, prove that AAT = I, where \[A = \begin{bmatrix}l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 \\ l_3 & m_3 & n_3\end{bmatrix}\]


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:

`[(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:

`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`


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:

`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`


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


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

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


If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.


If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is unit matrix of order 2


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


The matrix A `=[(0,1),(1,0)]` is a ____________.


The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]`  is a ____________.


If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.


Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements:

(P) If A1I2, then |A| = –1

(Q) If |A| = 1, then tr(A) = 2,

where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then ______.


If A and B are square matrices of order 3 × 3 and |A| = –1, |B| = 3, then |3AB| equals ______.


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 = `[(0, -tan  θ/2),(tan  θ/2, 0)]` and (I2 + A) (I2 – A)–1 = `[(a, -b),(b, a)]` then 13(a2 + b2) 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.


What is the order of a column matrix with \[m\] rows?


A matrix with only one row is called a:


What is the order of a row matrix with \[n\] columns?


If \[m=n\], what type and order does the matrix have?


An identity matrix (unit matrix) is a square matrix with:


What happens when any matrix is multiplied by an identity matrix?


Which matrix is a zero matrix?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×