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Problem Sheet #6 (2.2-2.4) ClassID: _____ Name: _________________________ Hmk. 6 Score _________ Math 1090 – 001 Spring 2013 Instructor: Katrina Johnson Complete each problem. No credit will be given without supporting work. 1. Using these matrices, perform the following calculations (or state that it’s not possible): ⎡ 1 −2 ⎤ A = ⎢ ⎥ ⎣−1 0 ⎦ ⎡5 3⎤ B = ⎢ ⎥ ⎣4 1 ⎦ a) AB € ⎡ 3 −2 2 ⎤ C = ⎢ ⎥ ⎣−1 2 1 ⎦ ⎡−1⎤ X = [ 4 −3] Y = ⎢ ⎥ ⎣ 2 ⎦ d) CA € € € e) BC b) XY c) YX ⎧ x + 2y − z = 5 ⎪ 2. ⎨ −x + 3z = −1 ⎪ ⎩ z + y − x = 4 a) Write the system of equations as an augmented matrix. € b) Write the system of equations as a matrix equation. € 3. Use Gauss-Jordan Elimination to solve the system of equations. ⎧ 3x − y = 1 ⎪ ⎨2x − y + z = 0 ⎪ ⎩ x + z = −1 € 4. Find the inverse of the matrix, or state that the inverse does not exist. ⎡1 0 1 ⎤ ⎢ ⎥ M = ⎢3 −1 0 ⎥ ⎢⎣2 −1 1 ⎥⎦ € 5. Solve the system of linear equations using an inverse matrix. ⎧2x + y = −2 ⎨ ⎩ 3x − y = 2 €