HW4_ENED1091_2018.docx - ENED 1091 Homework#4 Due Week of...

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ENED 1091: Homework #4 Due: Week of February 12 th at beginning of Recitation Problem 1 : Arithmetic Operations with Arrays Determine whether or not the following matrix operations are allowable or not. If the operation is not allowable, indicate this. Otherwise, provide the result. Do these by hand. (a) [ 4 8 1 2 A 3 ] + [ 5 2 6 B 7 1 ] = Undefined (b) [ 4 8 1 2 A 3 ] [ 5 2 6 B 7 1 ] = Undefined (c) [ 1 2 ] × [ 4 5 3 ] = 4 5 3 8 10 6 (d ) [ 5 3 0 ] × [ 2 6 0 ] = undefined (e) [ 2 0 3 5 ] × [ 4 0 A 5 3 B ][ 8 0 2 A 37 15 3 A + 5 B ] Problem 2 : Solving Systems of Linear Equations using Matrices Write each of the following systems of equations in matrix form: Ax = b. Then determine whether or not each of the following systems of linear equations has a unique solution. If there is a unique solution, find it. Include all MATLAB commands. (a) r + 2 s + 3 t = 1 2 r + 6 s + 2 t =− 1 10 s + 8 t = 3
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What is the Matrix Equation? Write it out in the form Ax = b. [ 1 2 3 2 6 2 0 10 8 ][ r s t ] = [ 1 1 3 ] What is the determinant of the matrix? 0 If there is a unique solution, then solve for r, s, and t. No solution clc clear A=[1 2 3;-2 6 2;0 10 8]; B=[1; -1; 3] if det(A) ~= 0 x=inv(A)*B; fprintf( 'x= %f' ,x) else fprintf( 'no solution' ) end (b) q r + 2 s + 3 t = 1 2 q + 4 r + 6 s + 2 t =− 1 7 q
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