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50 questions on linear algebra for NET and GATE aspirants - Gonit Sora (???? ?'??)
This set of Linear Algebra Multiple Choice Questions & Answers (MCQs) focuses on �Conversion from Cartesian, Cylindrical and Spherical Questions In Linear Algebra In Coordinates�. 1. Convert Cartesian coordinates (2, 6, 9) to Cylindrical and Spherical Coordinates. a) (, , ) and (11, , ) Questions In Linear Algebra 4th Edition b) (, , 9) and (, , ) c) (, , ) and (, , ) d) (, , 9) and (11, � Now, substituting the values for x as 2, y as 6 and z as 9, we get the answer as (, , 9) and (11, , ). advertisement. 2. Convert the (10, 90, 60) coordinates to Cartesian coordinates which are in Spherical coordinates. a) (5, , 10) b) (5, , 0) c) (10, 5, ) d) (0, 5, ) View Answer. Answers to Exercises. Linear Algebra Jim Hefferon. ? 1? 3. ?2? 1.� One.I This is how the answer was given in the cited source. Eight commissioners voted for B. To see this, we will use the given information to study how many voters chose each order of A, B, C. The six orders of preference are ABC, ACB, BAC, BCA, CAB, CBA; assume they receive a, b, c, d, e, f votes respectively.� The answer to this question would have been the same had we known only that at least 14 commissioners preferred B over C. The seemingly paradoxical nature of the commissioners�s preferences (A is preferred to B, and B is preferred to C, and C is preferred to A), an example of �non-transitive dominance�, is not uncommon when individual choices. Linear Algebra - Linear Algebra. Home. Engineering Mathematics. Linear Algebra. Linear Algebra. 1: Rank of the matrix A.� A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is. A. A must be invertible.� GAURAV SHARMA said: (pm on Friday 28th October ). |C|=0 so rank of C is <3 but there are no non-zero minors of order 2x2 so but there exists a 1x1 minor if any element in A and B is not zero then rank of C is 1. suraj said: (am on Tuesday 24th January ). rank should be 1.

Connect and share knowledge within a single location that is structured and easy to search. Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc.

For questions specifically concerning matrices, use the matrices tag. For questions specifically concerning matrix equations, use the matrix-equations tag. Stack Overflow for Teams � Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Questions tagged [linear-algebra]. Ask Question. Learn more� Top users Synonyms 1. Filter by. Sorted by. Tagged with. Apply filter. What's an intuitive way to think about the determinant? In my linear algebra class, we just talked about determinants.

Jamie Banks Singular value decomposition SVD and principal component analysis PCA are two eigenvalue methods used to reduce a high-dimensional data set into fewer dimensions while retaining important I do not understand anything more than the following.

Elementary row operations. Dilawar 5, 6 6 gold badges 23 23 silver badges 36 36 bronze badges. Ryan 4, 6 6 gold badges 17 17 silver badges 10 10 bronze badges. Eckhard 6, 3 3 gold badges 19 19 silver badges 28 28 bronze badges.

Hans Parshall 5, 3 3 gold badges 21 21 silver badges 29 29 bronze badges. Why do we care about dual spaces? When I first took linear algebra, we never learned about dual spaces. Today in lecture we discussed them and I understand what they are, but I don't really understand why we want to study them within WWright 4, 3 3 gold badges 27 27 silver badges 32 32 bronze badges. Why does this matrix give the derivative of a function?

Eigenvectors of real symmetric matrices are orthogonal Can someone point me to a paper, or show here, why symmetric matrices have orthogonal eigenvectors? Phonon 3, 4 4 gold badges 22 22 silver badges 27 27 bronze badges. How could we define the factorial of a matrix? How could we define the following operation? Turing What is the difference between linear and affine function I am a bit confused.

What is the difference between a linear and affine function? Any suggestions will be appreciated. How to intuitively understand eigenvalue and eigenvector? I'm learning multivariate analysis and I have learnt linear algebra for two semester when I was a freshman. Eigenvalue and eigenvector is easy to calculate and the concept is not difficult to Jill Clover 4, 7 7 gold badges 24 24 silver badges 45 45 bronze badges. What is the geometric interpretation of the transpose?

I can follow the definition of the transpose algebraically, i. Zed 1, 3 3 gold badges 11 11 silver badges 3 3 bronze badges. Moos Hueting 1, 3 3 gold badges 10 10 silver badges 10 10 bronze badges.

Are there theorems that help with calculating the inverse of the sum of matrices? Tomek Tarczynski 2, 4 4 gold badges 17 17 silver badges 17 17 bronze badges.

Proof that the trace of a matrix is the sum of its eigenvalues I have looked extensively for a proof on the internet but all of them were too obscure. I would appreciate if someone could lay out a simple proof for this important result.

Thank you. JohnK 5, 3 3 gold badges 22 22 silver badges 43 43 bronze badges. It would seem that one way of proving this would be to show the existence of non-algebraic numbers. Is there a simpler way to show this?

Elchanan Solomon Is the following matrix invertible? Yongkai 1, 3 3 gold badges 12 12 silver badges 7 7 bronze badges. I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current Where to start learning Linear Algebra? I'm mostly a corporate developer, and it's somewhat boring and non exciting.

When I began my career, I chose it because Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition? I'm trying to intuitively understand the difference between SVD and eigendecomposition.

From my understanding, eigendecomposition seeks to describe a linear transformation as a sequence of three During a year and half of studying Linear Algebra in academy, I have never questioned why we use the word "scalar" and not "number". When I started the course our professor said we would use "scalar" LiziPizi 2, 3 3 gold badges 14 14 silver badges 32 32 bronze badges. What is the difference between a point and a vector?

I understand that a vector has direction and magnitude whereas a point doesn't. However, in the course notes that I am using, it is stated that a point is the same as a vector. Also, can you do Why is the eigenvector of a covariance matrix equal to a principal component?

If I have a covariance matrix for a data set and I multiply it times one of it's eigenvectors. Let's say the eigenvector with the highest eigenvalue. The result is the eigenvector or a scaled Why study linear algebra? Simply as the title says. I've done some research, but still haven't arrived at an answer I am satisfied with. I know the answer varies in different fields, but in general, why would someone study AaronAAA 1, 2 2 gold badges 9 9 silver badges 7 7 bronze badges.

So I'm having a tough time figuring this one out. I know that I have to work with the characteristic Physical meaning of the null space of a matrix What is an intuitive meaning of the null space of a matrix? Why is it useful? I'm not looking for textbook definitions. My textbook gives me the definition, but I just don't "get" it. Is the inverse of a symmetric matrix also symmetric? I seem to remember a proof similar to this from my linear algebra class, When is matrix multiplication commutative?

I know that matrix multiplication in general is not commutative. Martin Thoma 8, 12 12 gold badges 52 52 silver badges bronze badges. Why is it important for a matrix to be square? I am currently trying to self-study linear algebra. I've noticed that a lot of the definitions for terms like eigenvectors, characteristic polynomials, determinants, and so on require a square Beneschan 2 2 gold badges 6 6 silver badges 10 10 bronze badges.

Why, historically, do we multiply matrices as we do? Why, intuitively, is the order reversed when taking the transpose of the product? Why are vector spaces not isomorphic to their duals? What does it mean to have a determinant equal to zero?

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