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## This Week

We solved some more linear systems and began a study of matrices. Updated notes.

## Exercise Solutions

**I will give the solution to the first part of a question and then the answers to remaining parts.**

### P. 21 Exercises

#### 1 (i)

Letting the first column be , the second and the third :

.

.

.

#### (ii)

#### 2 (i)

.

Hence and .

(ii) (iii) No solutions (iv) (v) for (vi) .

#### 3 (a)

No

has non-zero solutions. For example .

#### (b)

No. The above example is a counter-example.

#### (c)

No.

#### has a unique solution .

#### (d)

No.

has the unique solution .

### P. 29 Exercises

#### 1 (i)

Not possible — they are different sizes

(ii) (iii) (iv) Not possible. (v) (vi) Not possible.

#### 2 (i)

Adding to both sides:

.

.

.

(b) (c) (d)

#### Q. 3 (a)

These matrices are conformable:

(b) (c) (d) (e) Non-conformable (f)

#### 4 (a)

Suppose that is an matrix. Hence when we multiply we need (). is a square matrix.

(b) One is while the other is (c)

## 3 comments

Comments feed for this article

February 20, 2012 at 8:06 pm

Graham KHi JP,

Solution (iv) I think Z=-7/3 & y=10/9. I assume you just made a typo or am I missing something?

corrected – J.P.February 21, 2012 at 12:41 pm

Graham KHi JP, Questions on page 29. Q2(b) Why is T (transpose sign) in ans?

Q3(c) Should this be 1 0 top, 0 1 Bottom?

Q4(c) Is B a 3 * 5 ?

Rgrds,

Graham

February 21, 2012 at 12:51 pm

J.P. McCarthyGraham,

It’s easier to typeset (4\,\,1/2)^T rather than \left(\begin{array}{c}4\\ 1/2\end{array}\right).

Corrected.

Corrected.

Cheers,

J.P.