Science:Math Exam Resources/Courses/MATH152/April 2010/Question A 13

MATH152 April 2010

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Question A 13
Write the matrix A that would result from the following lines of MATLAB code: A = zeros(3,3); for i=1:2 A(i,i) = -5; A(i,i+1) = 1; end A(3,3) = -2;

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Hint
What is the dimension of A? Initially, all entries are 0. How many entries are changed in total? Which?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. The first line of code creates the 3 by 3 zeros matrix: $A=\left[{\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}}\right]$ Then we enter the for-loop. In the first iteration, the entry A(1,1) is set to -5 and A(1,2) is set to 1, resulting in $A=\left[{\begin{array}{ccc}{\color {green}-5}&{\color {green}1}&0\\0&0&0\\0&0&0\end{array}}\right]$ In the second iteration the entry A(2,2) is set to -5 and A(2,3) is set to 1, hence $A=\left[{\begin{array}{ccc}-5&1&0\\0&{\color {green}-5}&{\color {green}1}\\0&0&0\end{array}}\right]$ Finally, the entry A(3,3) is set to -2. So the final answer is $A=\left[{\begin{array}{ccc}-5&1&0\\0&-5&1\\0&0&-2\end{array}}\right]$