MAT1503 (Linear Algebra) Exam Questions And Answers. Verified and Updated.

MAT1503 (Linear Algebra) Exam Questions And Answers. Verified and Updated. Matrix - answerA rectangular array of numbers linear equation in n (j) unknowns - answera₁x₁ + a₂x₂ + ... + ax = b linear equation - answerx + 3y = 7 or x₁ − 2x₂ − 3x₃ + x₄ = -1 (no products or roots of variables) system of linear equations (linear system) - answerA finite set of linear equations solution of a linear equation - answerA sequence of numbers for which the substitution with variables will make the equation a true statement homogeneous linear equations - answerx₁ − 2x₂ − 3x₃ + x₄ = 0 solution of a linear system - answerThe element is a solution of each equation solution set (general solution) - answerAll solutions of a linear system with the number sequence as the elements ordered n-tuple - answerA linear solution written as (a₁, a₂, ... , a) ordered pair - answerordered n-tuple if n = 2 ordered triple - answerordered n-tuple if n = 3 consistent system - answerA linear system that has at least one solution equivalent systems - answerTwo systems of equations that have the same solution set inconsistent system - answerA linear system that has no solutions parameter - answerAn assigned arbitrary value where the linear system has infinite solutions parametric equations - answerThe solution expressed by the equations using parameters algebraic operations - answer1) Add a multiple of one equation to another 2) Multiply an equation by a nonzero constant 3) Interchange two equations EXAM STUDY MATERIALS July 24, 2024 1:33:58 PM Elementary Row Operations - answer1) Add a multiple of one row to another row 2) Multiply any row by a nonzero constant 3) Interchange two rows augmented matrix - answerAn abbreviation of a linear system in a rectangular array of numbers elementary matrix - answerA matrix that was (or could be) produced by performing a single Elementary Row Operation on an identity matrix identity matrix - answerA square matrix with 1's on the main diagonal and zeros everywhere else. Note A×I = A and I×A = A Row Echelon Form - answerA matrix that has leading ones on the main diagonal and zeros below the leading ones. Reduced Row Echelon Form - answerA matrix that has leading ones on the main diagonal and zeros above and below the leading ones. leading variables - answerThe variables corresponding to the leading 1's in the augmented matrix free variables - answerThe variables that can be assigned an arbitrary value Gaussian Elimination - answer1) Put the matrix in augmented matrix form 2) Use row operations to put the matrix in echelon form 3) Write the equations from the echelon form matrix 4) Solve the equations. Gauss-Jordan Elimination - answer1) Put the matrix in augmented matrix form 2) Use row operations to put the matrix in reduced echelon form 3) Write the equations from the echelon form matrix 4) Solve the equations. trivial solution - answerThe solutions of the homogeneous linear systems are 0 non-trivial solution - answerThe solutions of the homogeneous linear systems are infinite (free variables are used) Free Variable Theorem for Homogeneous Systems - answerIf a homogeneous linear system has n unknowns, and its augmented matrix has r nonzero rows in reduced row echelon form, then the system has n - r free variabl