ASE 211 - Homework 2 Due Jan. 30

# ASE 211 - Homework 2 Due Jan. 30 - solution Change A to the...

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ASE 211 Homework 2 Due: In class, Wednesday, January 30 th . 1. Given the matrices C = 5 3 7 6 0 - 4 3 10 5 8 9 - 7 B = 2 9 6 5 7 - 4 3 8 Multiply by hand C * B . Can you multiply B * C ? Is it the same as C * B ? Compute ( C * B ) T . Show that it is equal to B T * C T . 2. Given a column vector d = 2 - 5 7 3 Multiply C * d . Can you multiply B * d ? Why? What about B T * d ? 3. Consider the 2x2 system A x = " 1 - 1 - 1 1 #" x 1 x 2 # = " 5 - 2 # = b Does this system have a solution? Is the solution unique? Change A to " 1 - 1 - 1 2 # Now does the system have a unique solution? Solve the system by hand, and check your answer by showing A x = b . 4. Give an example of a 3x3 upper triangular matrix, and a 3x3 lower triangular matrix. Are upper triangular matrices always nonsingular? (Hint: Consider the zero matrix, O ) 5. Create a matlab script called “ yourname hw2.m” in which you enter C , B and d above, multiply C * B , B * C , B T * C T and C * d . Enter the matrix A and vector b and try to solve A x = b using the “back slash” command( \ ). You should see some kind of error message or a very strange

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Unformatted text preview: solution. Change A to the second matrix and solve A x = b again. This time it should give you an answer. Multiply A * x . It should equal b . Keep a diary of your matlab session and hand in your script and your diary. Notes : Any of the commands that you enter in the command window can be put into an m-le. Such an m-le is called a script. Entering commands into a script can save time because if you make a mistake, it is easier to x in the script than in the command window. To create a script click on the new m-le icon in the upper left corner of the matlab window. Enter your matlab commands as you would in the command window and save the m-le. To invoke the script, go to the command window and type the name of the script at the prompt. You should already have expience with this process from homework 1....
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ASE 211 - Homework 2 Due Jan. 30 - solution Change A to the...

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