Linked Questions

2
votes
2answers
997 views

Determinant of a n x n Matrix - Main Diagonal = 2, Sub- & Super-Diagonal = 1 [duplicate]

I'm stuck with this one - Any tips? The Problem: Let $n \in \mathbb{N}.$ The following $n \times n$ matrix: $$A = \left( \begin{array}{ccc} 2 & 1 & & & & ...\\ 1 & ...
1
vote
1answer
359 views

Determinant of an $n\times n$ matrix with 5's on the diagonal and 2's on the superdiagonal and subdiagonal [duplicate]

Possible Duplicate: Special determinant formula for a specific matrix How to find $\det A_n$ as a function of $n$? $$A_n=\begin{pmatrix} 5&2 &0& 0 & \ldots & 0\\ 2& 5&...
3
votes
2answers
234 views

Determinant tridiagonal matrix [duplicate]

Can anybody help me out with getting an expression of the values of $\lambda$ for a matrix $A$ for which $det(A-\lambda I)$ equals the determinant of a matrix with on the main diagonal $-\lambda$, on ...
1
vote
0answers
62 views

Determinant of the following n×n matrix: [duplicate]

Determinant of the following $n \times n$ matrix: $$\begin{pmatrix} 2\cos \theta& 1 & 0 & \ldots & \ldots & 0 \\ 1 & 2\cos \theta & 1 & \ddots & & \vdots \\ 0 &...
0
votes
0answers
38 views

Three diagonal matrix inverse condition [duplicate]

Let $a$ is a constant. For which condition(s) this matrix has an inverse? $$\left[ \begin{array}{cccccc} a & 1 & 0 & \cdots & & 0 \\ 1 & a & 1 & \cdots & & ...
1
vote
0answers
31 views

Simple matrix determinant expression [duplicate]

I'm currently resolving a problem, and I came across the following matrix for which I need an expression of the determinant. $$ \begin{matrix} a+1 & 1 & 1 & 1 & . & . & ...
0
votes
0answers
18 views

find a, b and c such that the matrix is singular [duplicate]

I'm given matrix N by N $$\begin{pmatrix}a & b & 0 & 0 & 0 & ... & 0 \\\ c & a & b & 0 & 0 & ... & 0 \\\ 0 & c & a & b & 0 &... &...
4
votes
2answers
3k views

Proving the determinant of a tridiagonal matrix with $-1, 2, -1$ on diagonal.

Let $A_n$ denote an $n \times n$ tridiagonal matrix. $$A_n=\begin{pmatrix}2 & -1 & & & 0 \\ -1 & 2 & -1 & & \\ & \ddots & \ddots & \ddots & \\ & &...
6
votes
1answer
3k views

Determinant of symmetric tridiagonal matrices

Given an $n\times n$ tridiagonal matrix $$A =\left(\begin{array}{ccccccc} d_1&a_1\\c_2&d_2&a_2\\&c_3&d_3&a_3\\&&&\ddots\\&&&&\ddots\\&&&...
5
votes
1answer
384 views

Determinant evaluation for matrix with $-1, 2, -1$ below/on/above diagonal [duplicate]

What is the trick for evaluating the determinant of this matrix? $$\begin{bmatrix} 2 & -1 \\ -1 & 2 & -1 \\ & -1 & 2 & -1 \\ && -1 & 2 & -1 \\ &&& -...
2
votes
0answers
805 views

Gaussian Elimination on Block Matrix

I have a large matrix, with possibly over 100,000,000 elements in it and I want to solve it quickly. I want to take advantage of the fact that the matrix is partitioned into a small number of unique ...
1
vote
2answers
134 views

How to solve these general $n \times n$ determinants?

How would you solve these two general determinants? $$ \begin{vmatrix} 2 & 1 & 0 & \cdots & 0 & 0 \\ 1 & 2 & 1 & \cdots & 0 & 0\\ ...
1
vote
1answer
53 views

Can this determinant expression ever equal $0$?

My issue is that when calculating the eigenvalues of a matrix, there are cases where the eigenvalue is $0$, and so I was trying to confirm this by calculating the determinant and checking when it is ...