Solve for A-1 in Matrix Equation w/A, I

  • Thread starter Thread starter rock.freak667
  • Start date Start date
  • Tags Tags
    Matrices
rock.freak667
Homework Helper
Messages
6,221
Reaction score
31

Homework Statement



A square matrix A satisfies the matrix equation A3-3A2+7A-2I=0.
If A-1 exists, find an expression for A-1 in terms of A and I

Homework Equations





The Attempt at a Solution



I just multiplied the matrix equation by A-1 and then rearranged to get

2A-1 =3A-7I-A2

Is it that easy? Or is there something that I am missing?
 
Physics news on Phys.org
Yes I suppose that is all, although you might want to check your signs.
 
ok thanks..will do.
 

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

Linear Algebra: Verifying A^2-2A+7I=0
Replies
3
Views
2K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
Replies
2
Views
1K
Finding inverse from matrix equation
Replies
3
Views
1K
Solving Complex Equations: z2+2(1-i)z+7i=0
Replies
3
Views
1K
Understanding Conditional Expectation, Variance, and Precision Matrices
Replies
0
Views
763
Solving a system of differential equations by fundamental matrix
Replies
8
Views
3K
Linear Algebra matrix linear transformation
Replies
7
Views
2K
Are Similar Matrices' Eigenvalues the Same? Solving for Symmetric Matrices
Replies
9
Views
2K
Stuck finding a specific value of an inverse of a complex matrix
Replies
1
Views
1K
Solving a first order matrix differential equation
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top