CALCULATION IN STATISTICS

Section 4.1

 

2.

The given vector can be written as

 

 

6.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10.

 

Therefore,

 

This is illustrated geometrically as shown below.

 

 

 

 

 

 

 

 

 

 

14.

 

 

Therefore,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

18.

 

 

(a)

 

(b)

 

(c)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

22.

 

Therefore,

 

 

 

30.

 

(a)   Therefore,

 

(b)

 

(c)

 

 

36.

 

Now,

 

 

42.

 

If v is a linear combination of u and w, then

 

Therefore,

 

 

 

Therefore,

 

Therefore,

 

 

46.

 

then

 

Therefore,

 

 

 

 

Therefore,

 

Therefore,

 

 

52. (a) to subtract two vectors in Rn, subtract their corresponding components.

The statement is True.

Since

 

 

(b)  The zero vector in Rn is defined as the additive inverse of a vector.

The statement is false,

Since,

 

54.

 

then

 

Therefore,

 

We suppose,

 

Therefore,

LI17

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