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**Unformatted text preview: **MATH 152 L1 & L2 Applied Linear Algebra and Diﬀerential Equations Week 08 Worksheet (March 21, 2005): Matrix
3 2 1 −3 = 2 4 2 . −2 Spring 2004-05 Q1. (Addition and scalar multiplication) Solve 3A − Q2. (Matrix multiplication) Simplify A [(3A − 7B) − (7A + 2B)] − (A − 2B) B. Q3. (Matrix equation) Let A = 1 −y x y and B = y 2x − 2x . 2 Find x, y such that BA = O. 00 Q4. (Inverse) Verify that A = 0 1 12 compute the inverses of A2 and At . 1 1 2 and B = −2 3 1 −2 1 0 1 0 are inverse to each other. Then 0 Q5. (Symmetric matrix) Show that if A is symmetric, then so are A−1 and At . Q6. (Augmented matrix) Write down the augmented matrix for the system of linear equations −x2 +4x3 = 2, x1 +2x3 = 5, 3x1 +2x2 = 1. Q7. (Augmented matrix) Write down the system of linear equations with the following matrix as the augmented matrix 0 0 5 2 3 0 2 0 1 −3 . 4 0 7 0 −2 0 −2 −5 9 1 Q8. (Gaussian elimination) Solve the system of linear equations 3x1 2x1 +2x2 +x2 +x3 −x3 = = 3, − 1. Q9. (Gaussian elimination) Solve the system of linear equations +x2 −2x3 = 1, x1 2x1 +3x2 −2x3 = −2, 3x1 −3x3 = 4. Q10. (Gaussian elimination) Find coeﬃcients a, b such that the line given by the equation ax1 + bx2 = 1 passes through the points (2, −3) and (1, −4). ...

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