Comment due Sunday, November 3
Test #2 will be given in class Monday, November 4. The format will be similar to the format of Test #1.
Recall from Test #1 that one question asked you a series of conceptual true/false questions where you had to justify your answer. Another question asked you for a series of examples of mathematical objects (mostly matrices) satisfying certain conditions.
To prepare for Test #2, for this week’s OpenLab assignment, you will comment on this post with two questions that you come up with yourself, as well as their answers.
- Your first question should be conceptual and phrased as a statement which is either always true or always false. Your answer should indicate whether the statement is true or false together with a sentence explaining the answer.
- Your second question should be asking for an example of a mathematical object satisfying certain conditions. Your answer should provide this example together with together with a sentence explaining the example and why it satisfies the conditions.
You can use the Test #1 questions for inspiration (the different versions of the tests had similar questions, so check out your classmates’ solutions for the other versions).
Try to focus on the material covered in class since Test #1. You can see the list of topics on the schedule.
Question 1: Is it true that k X i = j?
Answer: Yes. This is true because of the “Right-Hand System”, this system is used to determine if vectors are perpendicular to each other. You use your index finger to represent one vector, middle finger to represent another vector and thumb to represent the direction of the two vectors via cross product.
Question 2: Given the matrices a1=[-3,5,5], a2=[-5,-1,-6] and b=[11,-9,-6]. Is “b” within the spanning set of a1 and a1?
Answer: Yes matrix b is in the spanning set of a1 and a2 because it exist in the linear combination both matrix a1 and matrix a2. If the numbers of a1 were multiplied by 2, the a2 numbers were multiplied by -1 and added together they would create matrix b.