Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution.

1) Compute u + v and u - 2v

u = -1 ; v = -3
2 -1

2) Display the following vectors using arows on an xy graph: u, v, -v, -2v, u+v, u-v, and u-2v. Use u and v from #1.

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Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using ...

Solution Summary

Vector equations are expressed using matrices and graphs. The solution is well-presented.

Give a demonstration as to why or why not the given objects are vector subspaces of M22
a) all 2 X 2 matrices with integer entries
A vector space is a set that is closed under finite vector addition and scalar multiplication.
It is not a vector space, since V is NOT closed under finite scalar multiplication. For insta

1. Find the dot product for the following pairs of vectors:
a. Row vector = (2 0) Column vector is below
5
18
b. Row vector = (3 9 -4) Column vector is below
3
0
2
c. Row vector = (5 6 7 8)
1
1
1
1
The following matrices will be used in problems 2-3 below:
0 -2 5
A= 3 -4 17
1 2 3
9 7 2
-3

2. Use Theorem 5.2.1 to determine which of the following are subspaces of M22.
Thm 5.2.1: If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if the following conditions hold.
(a) If u and v are vectors in W, then u + v is in W.
(b) If k is any scalar and u is any vector in W,

1. Consider the system of equations
x + y + 2z = a
x + z = b
2x + y + 3z = c
Show that for this system to be consistent, the constants a, b, and c must satisfy c = a + b.
2. Show that the elementary row operations do not affect the solution set of a linear system.
3. Consider the system of equations
ax + by =

1. consider the following subspaces of R^4
V=span{v1,v2,v3}, W=span{w1,w2,w3}
where v1=(1,2,1,-2)^T w1=(1,1,1,1)^T
v2=(2,3,1,0)^T w2=(1,0,1,-1)^T
v3=(1,2,2,-3)^T w3=(1,3,0,-4)^T
a)Find two systems of homogeneous linear equations whose solution spaces are V and W, respectively.
b)Find a basis f

Gretchen Schmidt plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540. How many share of each stock should she buy?
Use the form of " AX=B " equation