Science:Math Exam Resources/Courses/MATH152/April 2022/Question A14/Solution 1

From UBC Wiki

Recall from the hint that a matrix will have first column , and second column , where and are the standard basis vectors and .

Now, note that , and use the property that for an eigenvalue-eigenvector pair to get

since . This results in the first column of simply being .

For the second column of , we first note that . Using the same eigenvalue-eigenvector relation we have

since . This results in the second column being , and the matrix is