Multivariable Mathematics With Maple- Linear Algebra, Vector by James A. Carlson

By James A. Carlson

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Example text

It consists of the key words do and od (that is, do spelled backwards) enclosing a list of instructions. In our case we have only one instruction — add the quantity 1/i^2 to the current value of total and then store the result in total. Running our loop is the same as executing the sequence of commands below. 0/i^2; Consequently, the counter i has the value 5 when the loop is complete. This may cause trouble later, so you might want to clear the variable i with i := ’i’ when you have finished the problem.

0/i^2; od; RETURN ( total ); end; Warning: As with loops, it is much safer to type the entire definition with a single prompt (>). With a small bit of extra work, we can devise a procedure which computes the nth partial sum Sn = f (1) + f (2) + . . + f (n) where f is an arbitrary function. 0; for i from 1 to n do total := total + evalf( f(i) ); od; [ n, total ]; end; The arguments of S are a function and a number. The function value S(f,n) is a list consisting of two items: the number of terms in the sum, and the value of the partial sum.

Are they the same? Compute A + B and B + A. Are they the same? Compute 7A. Define C to be the sum of A and B. Then compute C 2 and compare to A2 + 2AB + B 2 . Compute the determinants of A and of B. Where possible, compute the inverses of A and B. Compute Av where v = (1, 2, 3) as above. Is it possible to compute vA? Let x be an unknown vector and solve Bx = v. Exercise 4. Let A be the same matrix as in the previous exercise. Use augment and gaussjord to solve Ax = v, where v = (1, 2, 3). Repeat for Ax = w, where w = (−1, 4, 1).

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