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By P. B. Medawar

To these drawn to a lifestyles in technological know-how, Sir Peter Medawar, Nobel laureate, deflates the myths of invincibility, superiority and genius; as a substitute, he demonstrates it's common feel and an inquiring brain which are necessary to the scientist's calling.

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As to less academic things, you all know that the order in which things are done on a date makes a great deal of difference in the end results. Addition and multiplication, the two main binary compositions for the real numbers, are connected by 3. The distributive law x · (y + z) = x · y + x · z for any real numbers x, y, and z. The numbers 0 and 1 occupy special places in the real number system. They are known as identity elements for addition and multiplication, respectively. The essential algebraic properties of these elements are given below.

Consider the m × m matrix Compute all powers of N if m = 5. Can you predict what will happen for arbitrary m? 4 MATRIX ADDITION AND SCALAR MULTIPLICATION In the last section we defined a multiplication for matrices and investigated its properties. In this section we shall introduce and study two more arithmetic operations on matrices, addition and scalar multiplication. These operations will be seen to have properties very much like those of ordinary addition and multiplication (in the field ).

13. 7. Show that finding A– 1 amounts to solving the system AX = K with n different choices for K. ] 8. 11 to express ROW3(AB) as a linear combination of the rows of B. 12 to express Col2(AB) as a linear combination of the columns of A. 9. Show that AX = Y is equivalent to 10. Let A be n × n, and let Compute B2 and B3. 7 SPECIAL KINDS OF MATRICES We have already mentioned several special kinds of matrices: square, diagonal, scalar, identity, and zero matrices. In this section we briefly mention several other special classes of square matrices.

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