Question

Matrix A= -2 1 0

2 -3 4

5 -6 7

vector u= 1

2

1

a) Is the vector u in Null(A) Explain in detail why

b) Is the vectro u in Col( A) Explain in detail why

Answer #1

LINEAR ALGEBRA
For the matrix B=
1 -4 7 -5
0 1 -4 3
2 -6 6 -4
Find all x in R^4 that are mapped into the zero vector by the
transformation Bx.
Does the vector:
1
0
2
belong to the range of T? If it does, what is the pre-image of
this vector?

Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1).
Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).

Consider the matrix A=
−2−2 6]
[−2−3 5]
[3 4−8]
[−7−9 18
(all one matrix)
(a) How many rows ofAcontain a pivot position?
(b) Do the columns ofAspanR4?
(c) Does the equationA ~x=~b have a solution for
every~b∈R^4?
(d) Would the equation A~x=~0 have a nontrivial solution?
(e) Are the columns of A linearly independent?
(~x is vector x)

Given a matrix F = [3 6 7] [0 2 1] [2 3 4]. Use Cramer’s rule to
find the inverse matrix of F.
Given a matrix G = [1 2 4] [0 -3 1] [0 0 3]. Use Cramer’s rule
to find the inverse matrix of G.
Given a matrix H = [3 0 0] [-1 1 0] [-2 3 2]. Use Cramer’s rule
to find the inverse matrix of H.

a) Find the steady-state vector for the transition matrix.
.8
1
.2
0
x= ______
__________
b) Find the steady-state vector for the transition matrix.
1
7
4
7
6
7
3
7
These are fractions^
x= _____
________

Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the projection of u onto
v.
(b) Find the vector component of u orthogonal to
v.

let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9} with A
= {1, 2, 3, 5, 7} and B = {3, 4, 6, 7, 8, 9}
a.)Find (A ∩ B) C ∪ B
b.) Find Ac ∪ B.

Stem
Leaf
2
6
3
0, 7
4
0, 2, 6
5
1, 5, 7, 9, 9
6
0, 2, 5, 8
1) standard deviation:
2)Find Five-number summary of the data set
3). Draw a box plot that represents the data set

#2. For the matrix A = 1 2 1 2 3 7 4 7 9 find the
following. (a) The null space N (A) and a basis for N (A). (b) The
range space R(AT ) and a basis for R(AT )
. #3. Consider the vectors −→x = k − 6 2k 1 and −→y =
2k 3 4 . Find the number k such that the vectors...

1. Let T = {(1, 2), (1, 3), (2, 5), (3, 6), (4, 7)}. T : X ->
Y. X = {1, 2, 3, 4}, Y = {1, 2, 3, 4, 5, 6, 7}
a) Explain why T is or is not a function.
b) What is the domain of T?
c) What is the range of T?
d) Explain why T is or is not one-to one?

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