Dr. Mark V. Sapir

Class 14

Homework due Class 15.

1. Let A=(1,2,3,4,5), B=(2,1,3,4,4), C=(1,2,1,3,1), D=(2,1,3,1,1) be vectors from R⁵. Find all numbers x, y, z such that
   

   xA+yB+zC=D

   
   
2. Two continuous functions f,g:[0,1]--> R are called orthogonal if the inner product f*g is 0. Find a non-zero continuous function f(x) which is orthogonal to x². Find infinitely many such functions. (Use the Maple operation "int" to compute integrals of functions.)

Solutions

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No homework due Class 16

Solutions

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Pre-Test 1

Solutions

Solutions

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Class 16

Homework due Class 17.

1. Consider the set V of all 2-vectors and define two operatons:

   The sum: (a,b)+(c,d)=(a+c+1, b+d),

   The scalar multiplication: k(a,b)=(ka,kb).
   

   Is V a vector space?

2. Find a function f(x) from C[0,1] which is a scalar multiple of x² and whose norm is 1.

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