How Do Row Operations Affect Matrix Determinants?

  • Thread starter Thread starter LaraCroft
  • Start date Start date
  • Tags Tags
    Determinants
LaraCroft
Messages
14
Reaction score
0

Homework Statement


If the determinant of a 3 x 3 matrix A is det(A) = 10, and the matrix B is obtained by multiplying the third row by 8, then det(B) = ___?

If the determinant of a 5 x 5 matrix A is det(A) = 9, and the matrix C is obtained from A by swapping the second and fourth rows, then det(C) =___?

Homework Equations



Ok, so do I use a generic matrix, or what? SO confused...

The Attempt at a Solution

 
Physics news on Phys.org
Hi LaraCroft! :smile:

Useful tip: write out a few matrices (easy ones, with lots of zeros :wink:), and see what happens …

then you can set about proving why :smile:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Why is my calculation for the determinant of a matrix incorrect?
Replies
6
Views
2K
Proof regarding determinant of block matrices
Replies
5
Views
5K
How Do Matrix ODEs Relate to Determinants and Traces?
Replies
3
Views
2K
Easy Determinant Help: Solving Row Operations for Matrix | -9 is Wrong?
Replies
15
Views
2K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
Replies
2
Views
1K
Linear independence of Coordinate vectors as columns & rows
Replies
2
Views
2K
Determinant of a Block Lower Triangular Matrix
Replies
2
Views
5K
Determinant Problem: Show $\det B = \det A$
Replies
11
Views
2K
Eigenvalues and Eigenvectors: Finding the Roots of a Matrix
Replies
1
Views
2K
Linear Algebra, Find a matrix C st CA = B
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top