Abstract
This chapter focuses on simultaneous linear equations. The systems of simultaneous equations appear frequently in engineering and scientific problems. A system of simultaneous linear equations is consistent if it possesses at least one solution. If no solution exists, the system is inconsistent. The chapter discusses the method of Gaussian elimination and reviews the concepts of linearly independent vectors and rank of a matrix. It discusses a few important theorems on linear independence and dependence. A set of vectors is linearly dependent if one of the vectors is a linear combination of the others. Any set of vectors that contains the zero vector is linearly dependent. If a set of vectors is linearly independent, any subset of these vectors is also linearly independent. If a set of vectors is linearly dependent, then any larger set, containing this set, is also linearly dependent. The rank of a matrix A, designated r(A), is the order of the largest nonzero minor of A. The row rank of a matrix is the maximum number of linearly independent rows. Analogously, the column rank of a matrix is the maximum number of linearly independent columns.
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