Always explain your answers, the only exception is if you are asked to calculate something. If asked to give an example,

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Always Explain Your Answers The Only Exception Is If You Are Asked To Calculate Something If Asked To Give An Example 1 (105.46 KiB) Viewed 70 times

Always explain your answers, the only exception is if you are asked to calculate something. If asked to give an example, you have to explain why your example does what it is supposed to do. If asked to show or prove something I am expecting a proof. In this course, a proof is a sequence of assertions that follow one another logically where you explain why each assertion follows from the previous assertions. You always have to conclude in your proofs. For the first two homework you will be assigned a random partner to discuss the homework. Please arrange one time to meet outside class. 1. Let ū, Ü, Ű E R3 and c, d ER. Show that: (a) ū+(ū+ ) = (ū +ū) +ū. (b) (c+d)ũ = cũ + dũ. 2. An n x n matrix A is symmetric if AT = A. (a) Give an example of a 2 x 2 matrix that is symmetric matrix and a 2 x 2 matrix which is not symmetric. (b) Show that if A is a 2 x 2 matrix, then A+ AT is symmetric. (c) Show that if A and B are symmetric 2 x 2 matrices, then A + B is a symmetric matrix. (d) Give an example of two symmetric 2 x 2 matrices such that their product is not a symmetric matrix. Hint: Remember that (AB)? = BÌA".