All Questions
Tagged with gaussian-elimination determinant
22 questions
0
votes
1
answer
91
views
Updating a Matrix Determinant After Row Replacement
Given a square matrix A (of varying dimension), I am looking for an efficient algorithm or formula to recompute the determinant of that matrix if a row i is replaced with different values.
For example,...
- 121
0
votes
1
answer
37
views
Determinant at every step while finding matrix inverse
I've come to an intuitive conclusion that feels right and for which it seems there must be a proof, but I have been unable to locate one nor am I certain how to go about writing the proof. Therefore, ...
- 127
1
vote
0
answers
88
views
Determinant of a Matrix using Gauss Elimination, inconsistent answers
I have worked through finding the determinant of the following Matrix
$$
\begin{pmatrix}
6 & -1 & 0 & 4 \\
3 & 3 & -2 & 0 \\
0 & 1 & 8 & 6 \\
2 & 3 & 0 &...
1
vote
2
answers
427
views
Let $v_1 = (1, 0, 2), v_2 = (1, 1, a)$, and $v_3 = (a, 1, −1)$. Find the value(s) of $a$ for which $v_1, v_2$, and $v_3$ are linearly dependent
I'm struggling to solve this question without the use of the determinant (I'm not allowed to use it). I've tried setting up a matrix with the vectors and putting that matrix into reduced row echelon ...
0
votes
0
answers
65
views
Scale factor of the determinant: I'm blind (SOLVED)
I have the following matrix
$$A = \begin{pmatrix} 2 & 5 & 8 \\ 3 & 6 & 9 \\ 4 & 7 & 9 \end{pmatrix}$$
I already calculated the determinant with Laplace in two different ways, ...
- 3,521
0
votes
1
answer
44
views
Gaussian Elimination Elements $a^{(r)}_{ij}$
Let $A\in \mathbb{R}^{n\times n}$. We apply GE to it. Prove that:
$\begin{align}
a^{(r)}_{ij}&= a^{(r)}_{ij}=\frac{A\begin{pmatrix}
1 & 2 &\cdots & r & i \\
1 & 2 &...
1
vote
3
answers
69
views
Troubles on a determinat of a $4\times 4$ matrix
$$A = \left(
\begin{array}{cccc}
1 & 3 & 1 & 0 \\
1 & -1 & 2 & 1 \\
1 & 0 & 1 & 1 \\
0 & 1 & 0 & 2 \\
\end{array}
\right)$$
Its determinant is $7$ ...
- 3,521
0
votes
0
answers
1k
views
How would I convert this matrix to a system of equations?
Given a matrix
$$A =\begin{pmatrix}1& 1& 1\\−2& 1& 3\\3& 2& 1\end{pmatrix}$$
use Gaussian elimination to compute the determinant $\det(A)$ of $A$ and to solve
the system of ...
- 1
1
vote
1
answer
76
views
determinant of $4\times 4$ matrix by elimination
I am trying to find the determinant of this $4\times 4$ matrix.
I got the wrong answer but I can't find the mistake
The answer is supposed to be $-44$ but I got $-176$
the matrix
$$
\begin{bmatrix}
...
- 13
3
votes
2
answers
151
views
Find the determinant whose result is $(x-n)^{n+1}$
Find the determinant
$$
\left|\begin{array}{cccccc}{x} & {1} & {} & {} & {} & {} \\ {-n} & {x-2} & {2} & {} & {} & {} \\ {} & {-(n-1)} & {x-4} & {\...
- 5,064
1
vote
0
answers
318
views
Gaussian elimination in vector spaces
I've been working on a set of problems while learning matrix operations as well as vector spaces and subspaces. But now I have some doubts that go outside the general rule of thumb and I'm unable to ...
3
votes
0
answers
64
views
Show that the values of the following determinants are not zero without actually finding the exact values
$$\begin{bmatrix}
111 & 100 & 225 & 235\\
220 & 312 & 220 & 410\\
215 & 180 & 268 & 305\\
315 & 145 & 205 & 122
\end{bmatrix}$$
Guys is it enough to ...
- 107
-1
votes
1
answer
733
views
Gauss Jordan inverse matrix, row of all zeros
I'm using the Gauss Jordan method to find the inverse of this matrix: [ 2 4 10; 3 4 6; 4 4 2]
So, I set up this matrix on the left and the identity matrix on the right, and I reduce until I get the ...
- 1
1
vote
2
answers
683
views
For what values of $k$ does the determinant of this matrix 'vanish?'
\begin{bmatrix}
k & 1 & 4 \\
1 & k & 3 \\
1 & 0 & 1
\end{bmatrix}
So I think to co-factor expand along the 3rd row giving me
$$1(3-4k)-0+1(k^2-1)$$
Which I guess can ...
- 245
0
votes
2
answers
175
views
Determinant of $ 3\times 3$ matrix by using gauss
I am trying to calculate the determinant of the following matrix by performing Gaussian elimination. I know that the determinant is $1$ but I get the wrong result.
\begin{bmatrix}
1 & 1 & ...
- 319
1
vote
2
answers
720
views
How to solve a matrix system using Gauss elimination
$$\left(\begin{array}{ccc|c}
-1 & 2 & 1 & 3\\
3 & \alpha & -2 & \beta\\
-1 & 5 & 2 & 9
\end{array}\right)$$
I am struggling to solve this system $Ax=b$. I ...
- 11
3
votes
1
answer
16k
views
Using elementary row or column operations to compute a determinant
How do you use elementary row or column operations to find the determinant of the following matrix?
$$\begin{bmatrix} 1 & 7 & -3\\
1 &3 & 1\\
4&8&1\end{bmatrix}$$
3
votes
3
answers
17k
views
Row replacement operation not changing the determinant
Can someone prove why a row replacement operation does not change the determinant of a matrix?
**row replacement operation being adding one row to another or something of that sort
8
votes
2
answers
18k
views
Is the determinant of a RREF matrix equal to the determinant of the original matrix?
Prove or disprove: If $R$ is the reduced row echelon form (RREF) of $A$, then $\det A = \det R$, where $A$ is an $n \times n$ matrix.
1
vote
0
answers
512
views
Characteristic Polynomial Calculation
I have a problem in my homework in which I have to find the characteristic polynomial of the following matrix:
I know the final solution is:
However, my answer keeps getting wrong whenever I ...
- 2,791
2
votes
1
answer
900
views
Gauss Seidel Method - How do I avoid calculating $L^{-1}$?
I'm trying to write a matlab code that gets a diagonal dominant matrix $A$, vector $b$, and finds an approximate solution $x$ to $Ax=b$ using Gauss-Seidel Method.
I understand the theory.
Suppose $L$...
- 12.9k
1
vote
3
answers
4k
views
Finding determinant for matrix using upper triangle method
Here is an example of a matrix, and I'm trying to evaluate its determinant:
$$
\begin{pmatrix}
1 & 3 & 2 & 1 \\
0 & 1 & 4 & -4 \\
2 & 5 & -2 & 9 \\
3 & 7 & ...
- 11