3) Let -1 -3 A = -1 3.1) Explain / show why the eigenvalues of A are -1,2. 3.2) Show that a basis for the eigenspace corresponding to -1 is given by

Q: 4 3 1 let A = -1 1 -3 Find a basis for the eigenspace corresponding to the eigen- 4 9. value A= 3

A: given  A=423-11-3249 find a basis for the eigenspace corresponding to the eigenvalue λ=3

Q: Find a basis for the eigenspace of A associated with the given eigenvalue 2. -10 12 A = 2 = -2 -8 10

A: Take (A+2I)X=O, O is the null matrix.

Q: Find the basic eigenvectors of A corresponding to the eigenvalue 2. 19 24 A = -12 -15 0 2 = 1 || 12…

A:

Q: 2.3. Let A E cmxm be hermitian. An eigenvector of A is a nonzero vector X E em such that Ax = AX for…

A:

Q: Find a basis for the eigenspace corresponding to each listed eigenvalue of A below. A = 1 0 2 = 2,1…

A:

Q: Find a basis for the eigenspace of A associated with the given eigenvalue 2. 5 -3 8 A = 1 7,2 = 4 2…

A:

Q: Find a basis for the eigenspace corresponding to the eigenvalue. 1 -6 ,A =9 6 A = A basis for the…

A: Given,

Q: Find the Eigen values and Eigen vectors for: A = 2

A:

Q: Suppose the same X diagonalizes both A and B. They have the same eigenvectors in A= XA1x-1 and B=…

A:

Q: he basic eigenvectors of A corresponding to the -1 0 1 -2 6 -3 3 -6 2 = -1 0 12 -18 | 0 0 6 -9…

A:

Q: Find a basis for the eigenspace corresponding to each listed eigenvalue of A below. 2 1 A = ,2 = 2,3…

A:

Q: Find a basis for the eigenspace corresponding to each listed eigenval A-5,2

A:

Q: Find a basis for the eigenspace corresponding to the eigenvalue A = 4 of matrix A given by -- [¹9 [1…

A:

Q: Prove that if 1 is an eigenvalue of A, then the matrix A – cl has an eigenvalue of 1 - c.

A: As λ is an Eigen value of A, therefore A-λI=0 . To find the Eigen value of A-cI for a constant c.

Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 7 1 A = - 3 0-15,…

A:

Q: Find the basic eigenvectors of A corresponding to the eigenvalue 1. |-4 6 -4 6 0 A = 1 = 1 0 0-15…

A:

Q: .

A:

Q: Let A = ['3 7 4 An eigenvalue of A is 5. Which one of the following is a basis for the corresponding…

A:

Q: Find a basis for the eigenspace corresponding to the eigenvalue. 4 -3 -2 A = -2 9 4 ,2 = 3 3 5 A…

A: We have A=[4−3−2−294−135]λ=3A-Iλ=[4−λ−3−2−29−λ4−135−λ]=[1−3−2−264−132] eigen space corresponding to…

Q: ind a basis for the A = 3 eigenspace of 6 6 A -1 1 -2 4 7

A:

Q: Find a basis for the eigenspace corresponding to each listed eigenvalue. 7 A = 2 = 1, 5 - 3 - 1

A:

Q: Let -3 v1= -2,03 = be eigenvectors of the matrix A which correspond to the eigenvalues A1 =-4, d2=…

A:

Q: Find a basis for the eigenspace corresponding to the eigenvalue. 4 3 -2 A = 9 - 4 A= 3 -1-3 A basis…

A:

Q: Find the eigenvalues and bases for the eigenspace of the matris [4 -3 01 3 Lo 4 21

A: We have to find eigenvalue and bases for eigenspace of given matrix.

Q: Find a basis for the eigenspace corresponding to each listed eigenvalue of A below. - 1 0 - 3 A = -…

A: A=−10−3−54−3608λ=4,2,5 For eigenvector…

Q: Exercise 3.4.9: 9 -2-6 a) Compute eigenvalues and eigenvectors of A = 10 -2 -6 b) Find the general…

A:

Q: (a) Compute the eigenvalues and an orthonormal eigen-basis for the matrix 3 1 1 A 1 3 1 113 (3 0.2)

A: Since you have posted a multiple question according to guildlines I will solve first (a) question…

Q: c) Show that eigenvectors of [T]B exhibit an orthonormal basis of Rt.

A:

Q: Find the eigenvalues and eigenvectors of 2 0 0 0 3 0 0 05 and show that the eigenvectors is the…

A:

Q: Find a basis for the eigenspace of A corresponding to the eigenvalue >. -1 12 12 A 0-9 -8, λ= -1 = 0…

A: We have to find the basis for the eigenspace of given matrix A corresponding to the eigenvalue λ.…

Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 0-20 1 -12 0 A =…

A: Here, A=30-2051-1203-4-1204-2-122λ=2

Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 7 - 1 0 - 5 0 4 A…

A:

Q: 4 -1 .Verify that 5 is an eigenvalue of A and v is an eigenvector. Then 4 -1 -1 -1 4 orthogo¬nally…

A:

Q: In Question , show that x is an eigenvector of A and find the corresponding eigenvalue.

A: Given :          x = 3-12   and  A = 13-60-45-5181510-40-32   To show that x is an eigenvector of…

Q: 7. Let 3 0 0 A = |1 3 1 5 1 3 Compute the eigenvalues of A. Is A diagonalizable?

A:

Q: 7 1 -2 Show that A = 6 is an eigenvalue of A = eigenspace. -3 3 6 and find a basis for its 2 2

A: A=71-2-336222

Q: -1 (2) Is A= 4 an eigenvalue of 3 1 ? If so, find one corresponding eigenvector. -3 4 5 (3) Find a…

A:

Q: -2 and v2 = -4 -2) - Let A = -4 5. 2 , Vュー Verify that vi and v2 are %3D -2 eigenvectors of A. Then…

A:

Q: 24. Find a basis for the eigenspace corresponding to each listed eigenvalue. [10 -9 (a) A = [20 , A…

A: To find the eigenspace of the given matrices for the given eigenvalues.

Q: Let -1 2 -8 0 1 0 0 0 1 A = Find the eigenvalues, and bases for the eigenspaces.

A: We have to find the eigenvalues first.

Q: Find the Eigen values and Eigen vectors for: A = 2 2 1 3

A: We need to find Eigen value and eigen vector.

Q: Find a basis for the eigenspace of A associated with the given eigenvalue 2. -1 -4 A = -6 1 2 = 5 -6…

A:

Q: Let λ1, λ2, ..., λn the eigenvalues ​​of matrix A. Show that det(A) = λ1λ2...λn

A: i have used the fact that characteristics polynomial of matrix A is given by…

Q: The value of h for which the eigenspace for A = 9 is two-dimensional is h=

A: Given that, A=9-24-407h000920006

Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. 5 0 A = -1 0 1=4…

A:

Q: Find a basis for the eigenspace of A associated with the given eigenvalue 1. 1. -10 12 ,1 = -2 A =…

A:

Q: Is λ=4 an eigen value of [ 3 0 −1 2 3 1 −3 4 5 ] ? If so, find one corresponding eigen vector?

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.