English

Identify the following matrix is singular or non-singular? [75-47] - Mathematics and Statistics

Advertisements
Advertisements

Question

Identify the following matrix is singular or non-singular?

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

Sum

Solution

Let A = `[(7, 5),(-4, 7)]`

∴ |A| = `|(7, 5),(-4, 7)|`

= 49 + 20

= 69 ≠ 0

∴ A is a non-singular 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 for any 2 x 2 square matrix A, `A("adj"  "A") = [(8,0), (0,8)]`, then write the value of |A|


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


If A is a square matrix such that A2 = A, then (I + A)3 – 7 A is equal to ______.


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?


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


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


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:

`[9   sqrt(2)  -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:

`[(3, 0, 0),(0, 5, 0),(0, 0, 1/3)]`


Identify the following matrix is singular or non-singular?

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


Find k if the following matrix is singular:

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


Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.


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

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`


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)]`


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


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


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 


AB = AC ⇒ B = C for any three matrices of same order.


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


Show by an example that for A ≠ O, B ≠ O, AB = O


If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.


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 ____________.


For any square matrix A, AAT is a ____________.


If the matrix A `= [(5,2,"x"),("y",2,-3),(4, "t",-7)]` is a symmetric matrix, then find the value of x, y and t respectively.


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


`[(5sqrt(7) + sqrt(7)) + (4sqrt(7) + 8sqrt(7))] - (19)^2` = ?


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


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×