Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
This is the Exam of Linear Algebra which includes Largest Possible Rank, Matrix, Smallest, Possible Dimension, Matrix, Distance, Vector, Linear Transformation, Matrix etc. Key important points are: Interchanging Rows, Determinants, Properties, Obtained, Invertible, Basis, Dimension, Sets, Appropriate, Vector Space
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Name:
(a) det 4B
(b) det C where C is obtained from A by interchanging rows 1 and 3
(c) det AT^ BT
(d) det (AB)−^1 if AB is invertible. Otherwise, explain why AB is not invertible.
(a) Let W =
a − b + 2c 2 b + 2c + d 4 b + 4c + 2d a + b + 4c + d
:^ a, b, c, d^ are real numbers.
. Is W a subspace of R^4?
Explain.
(b) Let W =
a + b b − 2 b + 1
(^) : a, b are real numbers.
. Is W a subspace of R^3? Explain.
and then find all the eigenvalues by solving the charateristic equation.
(b) (3 points) The vector
is an eigenvector of the matrix
. Find the corresponding eigenvalue.
(c) (4 points) Find a non-zero vector in Nul A where A =
(d) (3 points) Let ~b 1 =
, ~b 2 =
, and ~b 3 =
(^) be vectors in R^3. Then
B = {~b 1 ,~b 2 ,~b 3 } is a basis for R^3. If [~x]B =
, then find ~x.
