Sample+Midterm+1 - Math 4 Sample Midterm 1 A= 1 2 2 4 Find the eigenvalues and corresponding eigenvectors for A Find the orthogonal matrix Q that is

# Sample+Midterm+1 - Math 4 Sample Midterm 1 A= 1 2 2 4 Find...

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Math 4 Sample Midterm 1 . A = 1 2 2 4 Find the eigenvalues and corresponding eigenvectors for A . Find the orthogonal matrix Q that is used to diagonalize A . 1
2 . A = 3 1 1 1 1 1 1 0 1 Calculate: trace ( A ) | A | adj ( A ) A 1 2
3 . A = 1 1 2 0 1 1 B = 1 1 2 2 1 1 x = 1 2 1 and y = 2 1 0 Compute: Rank ( B ) AB xy T x T y || 2 x + y || 3
4 . Let A be a square matrix such that AA T = I . Show that | A | = ± 1 . 5 . Prove that | AB | = | BA | . 6 . A = 3 0 1 0 1 1 0 0 2 0 1 2 1 2 0 1 Compute det ( A ) . 4
7 . Solve the system of equations by any method. 2 x 1 x 2 + x 3 = 7 x 1 2 x 3 + x 4 = 7 3 x 2 x 3 + 2 x 4 = 5 x 1 + 2 x 2 x 4 = 1 5
8 . u = 2 1 1 v = 1 0 3 w =
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