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2. (a) Establish the rule for the multiplication of matrices.

(b) Find the product of a determinant of the nth order and its reciprocal.

3. Find the square root of the skew-symmetric determinant of the 6th order.

4. Obtain an expression for the nth convergent to the general continued fraction, and from it deduce the rule for finding successive convergents.

5. Find the equation whose roots are the (a) cubes of those of x - x3 + 2x2 + 3x+1=0, (b) nth powers of those of x+p1x2-1x...=0.

6. a is an imaginary root of x"-10 when n is prime. Show that the other roots are a2, a3, . . . .a”. Explain to what extent this is true for n composite, illustrating with x12 - 1=0.

7. Solve (a) x8 = 1+i√3.

(b) x3-3x2+xo − 9x5 −9x3+x2 −3x+1=0.

8. Solve the general quartic by assuming a(a。x1+ 4a1x3+ ...)=(a ̧x2+2a1x+a2+2a90)2 − (2mx+n)2.

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as equation of the tangent to curve f(xy)=0.

(b) Find tangent to 2y+by+y=a at x11 4. Find the equation of the asymptote to

y3=x2 (2α—x).

5. Find the "p.r." equation of the curve r2-2a2 cos 20. 6. Find the volume generated by revolution about the r axis of the area included between the curves

r2 by and y2=ax.

7. Expand in terms of r as far as the expression,

log (1-x+x2).

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