Math 340 Worksheet 2 Section 1.1 Systems of Linear Equations Linear equation Linear system Solution Consistent/inconsistent Homogeneous/nonhomogeneous Trivial/nontrivial solution Geometric perspective Method of elimination Section 1.2 Matrices Matrix: an array of numbers – rows – columns – entries Vect o r s Operations on matrices: addition, scalar multiplication, subtraction, linear combination, transpose Section 1.3 Matrix Multiplication Dot product – norm Matrix multiplication Matrix-vector product (linear combination) Write a linear system in the matrix form – coefficient matrix – augmented matrixPractice Problems 1. Determine the value ofxso that0vw, where 134xvand211xw. 2. Let 120435Fand245014321E, ComputeTFEif possible.3. Letcos sinsin cosA. (a) Determine a simple expression for2A. (b) Determine a simple expression for3A. (c) Conjecture the form of a simple expression forkA. k a positive integer. (d) Prove or disprove your conjecture in part (c). 4. Let 23412 3512Aand214c. ExpressAcas a linear combination of the columns of
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