1 2 2 and define Q : R² → >R by Q(x) = x" Ax. (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A. (c) Find a basis for each eigenspace of A.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Need help with this question. Thank you :)
![[1 2
8. Let A =
and define Q : R²
→ R by Q(x) = x"Ax.
2 1
(a) Find the characteristic polynomial of A.
(b) Find the eigenvalues of A.
(c) Find a basis for each eigenspace of A.
(d) For each eigenvalue, state its algebraic and geometric multiplicity.
(e) Is A orthogonally diagonalizable? If so, find a matrix P which orthogonally diagonalizes A.
(f) Is the quadratic form Q positive definite, negative definite, or neither?
(g) Is the conic section defined by the equation Q(x) = 1 an ellipse or an hyperbola? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb672f7-47ed-4ee3-be4e-71db737c6150%2F1fd979d6-b71b-4e41-90ac-c93b8643d334%2F406t6cm_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 6 steps with 50 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)