119 Answered Questions for the topic matrices

Is the rank of a matrix the same of its transpose? If yes, how can I prove it?

I am auditing a Linear Algebra class, and today we were taught about the rank of a matrix. The definition was given from the row point of view: > "The rank of a matrix A is the number > of... more


How do I exactly project a vector onto a subspace?

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I am... more


If I generate a random matrix what is the probability of it to be singular?

Just a random question which came to my mind while watching a linear algebra lecture online. The lecturer said that MATLAB always generates non-singular matrices. I wish to know that in the space... more

Must eigenvalues be numbers?

This is more a conceptual question than any other kind. As far as I know, one can define matrices over arbitrary fields, and so do linear algebra in different settings than in the typical... more


if the three schools have a total enrollment of 96,000 students, what is the enrollment at each school?

The University of Texas at Austin has three times as many students enrolled as the University of Miami. The University of California, Berkley has 3,000 more than twice the number of students as the... more

Can one factor matrices?

I know that one can factor integers as a product of prime numbers. Is there an analog of it to matrices? Can we define prime matrices such that every matrix is a product of prime matrices? Is there... more

orthogonal eigenvectors?

I have a very simple question that can be stated without proof. Are all eigenvectors, of any matrix, always orthogonal? I am trying to understand Principal components and it is cruucial for me to... more

Do all square matrices have eigenvectors?

I came across a video lecture in which the professor stated that there may or may not be any eigenvectors for a given linear transformation. And, so far I thought every matrix has eigenvectors.... more

Use of determinants?

I have been teaching myself maths (primarily calculus) throughout this and last year, and was stumped with the use of determinants. In the math textbooks I have, they simply show how to compute a... more

What are some applications of elementary linear algebra outside of math?

I'm TAing linear algebra next quarter, and it strikes me that I only know one example of an application I can present to my students. I'm looking for applications of elementary linear algebra... more
Matrices Calculus


How do you determine the dimensions of a matrix?

Determine the dimensions of the matrix2355


Matrices question. PLSSSSS HELP.

4. Let n≥2, let A and B b en×n matrices and let On be the n×n matrix with every entry 0.(b) Suppose that A2 = On. Show that In − A is invertible, and that (In − A)-1 = In + A.(c) Suppose that Am =... more

How to determine whether T is linearly independent ? Justify your answer please.

Let S={X1,X2,X3} be a linearly independent set of vectors in R^3. How to determine whether T={2X1 + X2 - 2X3,4X1+ 3X2,3X1 + 2X2 - X3} is linearly independent. Justify your answer please.


determine how much is borrowed at each rate given

A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 7%, some at 8.5%, and some at 9.5%. Use a system of linear equations... more


Use matrices to solve the system of linear equations

Use matrices to solve the system of linear equations, if possible. Use Gauss-Jordan elimination. (If not possible, enter IMPOSSIBLE. If the system is dependent, express x and y in terms of the... more


Write the system as a matrix equation and solve using inverses.

2x1 + x2 = 2 5x1 + 3x2 = 13   Write the system as a matrix equation and solve using inverses.  


Use algebra to solve for X in the matrix.

This is a 2x2 matrices problem. However, I am unable to type the matrices symbol in so I wrote it out.   Given A = 7  ,   x (top row) 15  ,  22 (bottom row). and the determinant for matrix A is... more


Step by Step equation on Matrix

3x -y - z = 4 x + y + 2z = 1 4x - y + z = 0


I need help understanding special cases in matrices

I need to solve this system of equations using a matrix: x+2y-z=2 , -2x+y-3z=6 , -x+3y-4z=8   I wound up with my matrix looking like this before I converted it back into equations again:      ... more


Solve for matrices 3x-y=2 x+2y=10

step by step please? 
Matrices Limits Analysis


Tough analysis related question - please help!

Let A= a b           c  d   be an arbitrary 2x2 matrix. Let xn ⊆ R2 and suppose that (xn)→x for some x∈R2. Prove that (Axn)→Ax


If Z and R are both inverse of matrix A, prove that Z=R

If Z and R are both inverse of the matrix A, prove that Z=R

solve the system of equations using the Gauss Jordan Method (2 problems)

label the augmented matrix(A:I), the resulting inverse(I:A^-1), column vector B, column vector of variables X, such that A^-1B=x   3x-5y=-5 6x-11y=-14     along with another problem which... more

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