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xiii Note to the reader: This is a customized book for Old Dominion ...
xiii Note to the reader: This is a customized book for Old Dominion ...
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SIMULTANEOUS LINEAR EQUATIONS 179Physical problemsChapter 04.00A Physical problem - general engineering 179Chapter 04.00B Physical problem - chemical engineeringChapter 04.00C Physical problem - civil engineering 182Chapter 04.00D Physical problem - computer engineeringChapter 04.00E Physical problem - electrical engineeringChapter 04.00F Physical problem – industrial engineeringChapter 04.00G Physical problem - mechanical engineering 187Chapter 4.1 Introduction <strong>to</strong> matrix algebra 193What does a matrix look like?What <strong>is</strong> a matrix? 193What are <strong>the</strong> special types of matrices? 194Square matrix 195Upper triangular matrix 195Lower triangular matrix 195Diagonal matrix 196Identity matrix 196Zero matrix 196Tridiagonal matrices 197When are two matrices considered <strong>to</strong> be equal? 197How do you add two matrices? 198How do you subtract two matrices? 199How do I multiply two matrices? 200What <strong>is</strong> a scalar product of a constant and a matrix? 202What <strong>is</strong> a linear combination of matrices? 203What are some of <strong>the</strong> rules of binary matrix operations? 203Transpose of a matrix 205Symmetric matrix 206Matrix algebra <strong>is</strong> used <strong>for</strong> solving system of equations. Can you illustrate th<strong>is</strong> concept?206Can you divide two matrices? 208Can I use <strong>the</strong> concept of <strong>the</strong> inverse of a matrix <strong>to</strong> find <strong>the</strong> solution of a set of equations[A] [X] = [C]? 209How do I find <strong>the</strong> inverse of a matrix? 209If <strong>the</strong> inverse of a square matrix [A] ex<strong>is</strong>ts, <strong>is</strong> it unique? 212Multiple-choice test 214Problem set 216Chapter 04.02 Vec<strong>to</strong>rsWhat <strong>is</strong> a vec<strong>to</strong>r?When are two vec<strong>to</strong>rs equal?How do you add two vec<strong>to</strong>rs?What <strong>is</strong> a null vec<strong>to</strong>r?What <strong>is</strong> a unit vec<strong>to</strong>r?How do you multiply a vec<strong>to</strong>r by a scalar?What do you mean by a linear combination of vec<strong>to</strong>rs?What do you mean by vec<strong>to</strong>rs being linearly independent?xvi