हिंदी

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

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • 2|A|

  • 4|A|

  • 8|A|

  • 6|A|

MCQ
रिक्त स्थान भरें
Advertisements

उत्तर

If A is a square matrix of order 3, then |2A| is equal to 8|A|.

Explanation:

Order of square matrix A.

n = 3

∵ |kA| = kn|A|,

k = constant

`\implies` |2A| = 23|A|

= 8|A|

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2022-2023 (March) Official

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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 a, b, c and d from the equation:

`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`


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


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


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


Use product `[(1,-1,2),(0,2,-3),(3,-2,4)][(-2,0,1),(9,2,-3),(6,1,-2)]` to solve the system of equations x + 3z = 9, −x + 2y − 2z = 4, 2x − 3y + 4z = −3


if the matrix A =`[(0,a,-3),(2,0,-1),(b,1,0)]` is skew symmetric, Find the value of 'a' and 'b'


In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.


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.


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:

`[(2, 0, 0),(3, -1, 0),(-7, 3, 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:

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


Identify the following matrix is singular or non-singular?

`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`


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:

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


Construct the matrix A = [aij]3 × 3 where aij = i − j. State whether A is symmetric or skew-symmetric.


Select the correct option from the given alternatives:

Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______


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 and B are matrices of same order, then (3A –2B)′ is equal to______.


For the non singular matrix A, (A′)–1 = (A–1)′.


If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`


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


If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.


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


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


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


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


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


Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.


If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.


A matrix with only one column is called a:


What is the order of \[B=\begin{bmatrix}-\dfrac{1}{2}&\sqrt{5}&2&3\end{bmatrix}\]?


Which matrix is a diagonal matrix?


Which statement correctly describes the relationship between scalar matrices and diagonal matrices?


Which condition defines an identity matrix?


What role does the zero matrix play in matrix algebra?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×