English

A=[aij]m×n is a square matrix, if ______. - Mathematics

Advertisements
Advertisements

Question

`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.

Options

  • m < n

  • m > n

  • m = n

  • None of these

MCQ
Fill in the Blanks

Solution

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

Explanation:

It is known that a given matrix is said to be a square matrix if the number of rows is equal to the number of columns.

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Matrices - Exercise 3.1 [Page 65]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 3 Matrices
Exercise 3.1 | Q 8 | Page 65

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)]`


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

`[(x+y, 2),(5+z, xy)] = [(6,2), (5,8)]`


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

`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`


If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB" = B"A. Further, prove that (AB)" = A"B" for all n ∈ N


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


Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.


Find the non-singular matrices P & Q such that PAQ is in normal form where`[(1,2,3,4),(2,1,4,3),(3,0,5,-10)]`

 


Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`


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:

`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`


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, 0, 1),(0, 1, 0),(1, 0, 0)]`


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:

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


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, 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.


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


Choose the correct alternative:

If B = `[(6, 3),(-2, "k")]` is singular matrix, then the value of k is ______


State whether the following statement is True or False:

If `[(3, 0),(0, 2)][(x),(y)] = [(3),(2)]`, then x = 1 and y = – 1


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


The matrix A = `[(0, 0, 5),(0, 5, 0),(5, 0, 0)]` is a ______.


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


If A `= [("cos x", - "sin x"),("sin x", "cos x")]`, find AAT.


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


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


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


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


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 ______.


The minimum number of zeros in an upper triangular matrix will be ______.


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


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


If `A = [(1,-1,2),(0,-1,3)], B = [(-2,1),(3,-1),(0,2)],` then AB is a singular matrix.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×