# pset1 - Do problem 27 in section 2.3 (pg. 55) Problem 10:...

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18.06 Problem Set 1 Due Wednesday, 13 February 2008 at 4 pm in 2-106. Problem 1: Do problem 28 from section 1.1 (pg. 10) in the book. Problem 2: Do problem 31 from section 1.2 (pg. 20). Problem 3: For the system A x = b (where A is a 3-by-3 matrix), choose A and b so that: 1. (row picture) the three planes meet in a common line 2. (row picture) all three planes are parallel but distinct 3. (row picture) the intersection of the ﬁrst two planes does not intersect the third plane 4. (column picture) b is not a linear combination of the columns of A 5. (column picture) b is a multiple of the second column of A Problem 4: Do problem 5 from section 2.2 (pg. 42). Problem 5: Do problem 12 from section 2.2 (pg. 43). Problem 6: Do problem 19 from section 2.2 (pg. 44). Problem 7: Do problem 23 from section 2.3 (pg. 54). Problem 8: Deﬁne the matrix A = 1 0 2 2 - 1 3 4 1 8 . Find a matrix B so that BA is upper triangular. (Hint: ﬁrst ﬁnd the elimination matrices for A .) 1

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Unformatted text preview: Do problem 27 in section 2.3 (pg. 55) Problem 10: Let’s do a warm-up Matlab question. Please include a printout of your Matlab code with your problem set! You can type diary(’ﬁlename’) at the beginning of your session to save a transcript, and diary oﬀ when you’re done. Let’s check that in general the products of matrices AB and BA are not equal. (However, as we’ll see later, some properties of the two products are the same.) We start with matrices of diﬀerent sizes. Type in the commands A=ones(3,2) and B=ones(2,3) (that is, A and B are the 3-by-2 and 2-by-3 matrices with all entries equal to 1). Compute A*B and B*A . What are their sizes? Now multiply 3 by 3 matrices C (your choice) and a random D (use the command D = rand(3,3) ). Does CD = DC ? Do their diagonals have the same sum (this is called the trace)? Find inv(C) and inv(D). 2...
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## This note was uploaded on 08/10/2008 for the course MATH 250 taught by Professor Chanillo during the Spring '08 term at Rutgers.

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pset1 - Do problem 27 in section 2.3 (pg. 55) Problem 10:...

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