I quite agree to it. On the contrary. Far from it

1. A matrix is a set of quantities arranged in rows and columns to form a rectangular array.

2. Simultaneous equations can be solved by means of matrices.

3. Only two types of matrices are considered in mathematics.

4. Matrices of complex numbers are derived from orthogonal ones.

5. The horizontal lines in a matrix are called columns.

6. Matrices are applied only in mathematics.

Ex. 7. Fill in the blanks with the necessary words and word combinations given bellow. Mind there are two extra ones.

a. finite-dimensional linear isometries b. a linear transformation c. an orthogonal group d. a unitary matrix e. the special orthogonal group f. determinant

g. orthogonal unit vectors h. spaces i. orthogonal j. an orthogonal matrix k. inner products l. a transpose

1. In algebra a square matrix is …with real entries whose columns and rows are ….

2. The set of n × n orthogonal matrices forms a group O (n) known as ….

3. An orthogonal matrix is the real specialization of….

4. Orthogonal matrices arise naturally from….

5. Thus … – rotations, reflections, and their combinations – produce orthogonal matrices.

6. Linear algebra includes orthogonal transformations between ….

7. The inverse of every orthogonal matrix is again....

8. The orthogonal matrices whose …is +1 form ….

Ex. 8. Match the left and the right parts of the following statements.

1. A matrix consists of 2. A matrix of m rows and n columns 3. The remainder of the last column 4. A square matrix is an orthogonal matrix 5. A series of such reflections 6. Matrices are important for

a. both theoretical and practical reasons b. with real entries c. must be zeros d. row vectors and column vectors e. is called an (mn) matrix f. can bring any orthogonal matrix to the identity

Ex. 9. Let us revise all tenses in the Active and Passive Voice.

1. You can borrow my dictionary. I (use) it a lot but I (not use) it now.

2. A lot of new houses(built) nowadays in Belarus provinces.

3. Helen (travel) to Kiev next month to attend a conference.

4. A new underground station (complete) in Minsk by 2014.

5. I (meet) my group-mate when I (go) to university yesterday.

6. A new drug for cancer (find) last year.

7. They (make) two attempts to pass the exam in algebra this week.

8. A new university campus (open) in a week.

9. Mr. Grey (work) for a software company for 20 years already.

10. The workshop on mechanical modelling (be held) tomorrow.

Ex. 10. Translate the sentences according to the models.

Model 1: One can – можно (One can use this numerical method.

Можно воспользоваться этим числовым методом.)

One cannot (one can’t) – Невозможно (One can’t swim a few miles without having a pause. Невозможно плыть несколько миль не отдыхая.)

1. One can speak many languages.

2. One can have a few jobs at a time.

3. One can take exams in advance.

4. One can’t be back into the childhood.

Model 2: One has to – необходимо (One has to remember the relationship between these facts. Необходимо помнить о соотношении этих фактов.)

One doesn’t have to – нельзя (One doesn’t have to cross the road at a red light. Нельзя переходить дорогу на красный свет.)

1. One has to sleep seven hours at night at least.

2. One has to bear in mind the formulae while solving equations.

3. This week one has to work longer hours.

4. One doesn’t have to drive without having a driving license.

Model 3: One needs – необходимо (One needs to mend the roof. Необходимо починить крышу.)

One doesn’t need – нет необходимости ( One doesn’t need to come here every day. Нет необходимости приходить сюда каждый день.)

1. One needs to inform them about the cancellation of the conference.

2. One doesn’t need to drive fast. There is plenty of time.

3. One doesn’t need to take an umbrella. It is not raining.

Model 4: One may – можно (Оne may work in the reading hall at any time. В читальном зале можно работать в любое время.)

One may not – нельзя (One may not feed animals in zoos. Нельзя кормить животных в зоопарке.)

1. One may get a free museum admission on Sundays.

2. Next Saturday one may have lectures by choice.

3. I don’t know if one may or may not leave this place at nights.

4. One may not smoke aboard the plane.

Model 5: One must – необходимо (One must invite her for a meeting. Необходимо пригласить ее на встречу.)

One must not (one mustn’t) - нельзя (I’m sure that one mustn’t be rude to anybody. Я уверен, что нельзя быть грубым ни с кем.)

1. One mustn’t be late for an appointment.

2. Tomorrow one must come to university half an hour earlier than today.

3. One mustn’t pollute the environment.

Model 6: One should – следует, надо (One should go to the dentist twice a year. К дантисту следует ходить два раза в год.)

One should not (one shouldn’t) – нельзя (One shouldn’t put such questions. Нельзя (не следует) задавать такие вопросы.)

1. One should be more careful while writing a dictation.

2. One should think over the plan once again.

3. One shouldn’t leave little children alone.