5. Consider the system of linear equations (a and b are real parameters): ax + y = 2 x+ ay = 6 a. Under which conditions on a and b does this system have a unique solution? Justify your answer. Find...

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5. Consider the system of linear equations (a and b are real parameters):<br>ax + y<br>= 2<br>x+ ay<br>= 6<br>a. Under which conditions on a and b does this system have a unique solution? Justify<br>your answer. Find the unique solution as a function of the parameters a and b.<br>b. Under which conditions on a and b does this system have no solutions? Justify your<br>answer.<br>c. Under which conditions on a and b does this system have infinitely many solutions?<br>Justify your answer.<br>d. Find the eigenvalues of the matrix:<br>(:)<br>1 3<br>A =<br>3 1<br>e. Find the eigenvectors of the matrix:<br>1 3<br>3 1<br>(::)--<br>Are the eigenvectors orthogonal?<br>

Extracted text: 5. Consider the system of linear equations (a and b are real parameters): ax + y = 2 x+ ay = 6 a. Under which conditions on a and b does this system have a unique solution? Justify your answer. Find the unique solution as a function of the parameters a and b. b. Under which conditions on a and b does this system have no solutions? Justify your answer. c. Under which conditions on a and b does this system have infinitely many solutions? Justify your answer. d. Find the eigenvalues of the matrix: (:) 1 3 A = 3 1 e. Find the eigenvectors of the matrix: 1 3 3 1 (::)-- Are the eigenvectors orthogonal?

Jun 04, 2022

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5. Consider the system of linear equations (a and b are real parameters): ax + y = 2 x+ ay = 6 a. Under which conditions on a and b does this system have a unique solution? Justify your answer. Find...

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