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# 2JSM2 - SECOND SAMPLE MIDTERM FOR MATH 2J This sample 2J...

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SECOND SAMPLE MIDTERM FOR MATH 2J This sample 2J midterm exam is meant for practice only. Length and content of the actual midterm may vary, at the discretion of the instructor. Try to complete the test in 50 minutes, without consulting any book or notes, and without using a calculator. 1

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2 Problem 1 Use Gaussian elimination to solve the linear system: x 1 + 2 x 3 + x 4 = 0 2 x 1 + 3 x 2 + 7 x 3 + 5 x 4 = 3 - x 1 - 2 x 2 - x 4 = 0 .
3 Problem 2 a Find the determinant of the matrix A = 3 4 3 - 2 0 2 3 4 0 0 1 0 0 - 2 0 1 . b Check your answer to part a ) by computing the same determinant in a different way. c Let B be a 6 × 6 matrix with determinant 3. Find: c1. The determinant of the matrix B 2 c2. The determinant of the matrix B - 1 .

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4 Problem 3 The matrix A = 0 0 1 0 1 0 0 0 1 has eigenvalues 0, 1, 1. a Find the corresponding eigenvectors. b Decide whether A is diagonalizable.
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2JSM2 - SECOND SAMPLE MIDTERM FOR MATH 2J This sample 2J...

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