1. what (5 pts) True or False and and justify to get full points (a) A vector in

ID: 2961215 • Letter: 1

Question

1. what (5 pts) True or False and and justify to get full points

(a) A vector in R4 comprises 4 complex numbers

(b) A dot product between two vectors results in vector that is perpendicular to the other two.

(d) If Ax = 0 then x lies in the null space of A

(e) The sum of the column rank and the row rank of a m x n (m is not equal to n) matrix is n+m

2) Answer all:

(a) Let the unit vectors be denoted by ^e1 = (1, 0) and ^e2 = (0, 1). Express the vector a = (4, 5) in terms of these unit vectors.

b) Suppose the unit vectors are ^e1 = (1, 1) and ^e2 = (-1, 1) express a = (4, 5) in terms of these unit vectors.

(d) Suppose the inner product is defined as (a) under multiplication (b) = a1b1 + 5a2b2 + a3b4 - a4b3. Does this define a vector space?

1) F may be real numbers

b)F dot product is scalar quantity

3) F co ordinate are (rcos theta , r sin theta , z ) it depends upon z

4) T by defination of null space

5) F it may be less than m+n

A)4e1+5e2

B) a*(1,1)+b(-1,1) =(4,5)

a-b=4

a+b=5

so, 2a=9

a=4.5

b= 4.5-4=.5

so answer is 4.5e1+.5e2

c) a.b = a*b*cos theta

a= (9.74)

b= 7.34

1*3+2*4+3*2+9*5 = 9.74*7.34 cos theta

theta = 30

d)yes it is multiplication of a row matrix and a column matrix

row matrix= (a1,a2,a3,a4)

and column matrix = (b1,5b2,b4,-b3)

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