हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • m < n

  • m > n

  • m = n

  • None of these

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

`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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Matrices - Exercise 3.1 [पृष्ठ ६५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 3 Matrices
Exercise 3.1 | Q 8 | पृष्ठ ६५

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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

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


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


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.


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


A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?


If 𝒙 = r cos θ and y= r sin θ prove that JJ-1=1.


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


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)]`

 


If\[A = \begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}\]prove that A − AT is a skew-symmetric matrix.


If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.


if  `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`


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


Identify the following matrix is singular or non-singular?

`[(7, 5),(-4, 7)]`


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.


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.


Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?


Choose the correct alternative:

If A = `[(2, 0),(0, 2)]`, then A2 – 3I = ______


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


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 A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2 


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


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


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


`root(3)(4663) + 349` = ? ÷ 21.003


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


The number of all possible matrices of order 3/3, with each entry 0 or 1 is


If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to


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


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


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 the sides a, b, c of ΔABC satisfy the equation 4x3 – 24x2 + 47x – 30 = 0 and `|(a^2, (s - a)^2, (s - a)^2),((s - b)^2, b^2, (s - b)^2),((s - c)^2, (s - c)^2, c^2)| = p^2/q` where p and q are co-prime and s is semiperimeter of ΔABC, then the value of (p – q) is ______.


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×