Row echelon form - Study guides, Class notes & Summaries

System of Equations: Consistent/Inconsistent Has a solution (or many)= Consistent No solution= inconsistent Matrices: Echelon Form Requirements 1. All nonzero rows are above zero rows 2. each leading entry of a row is in a column to the right of the leading entry of the row above it 3. all entries in a column below a leading entry are 0s Matrices: Reduced Echelon Form Requirements all 3 of Echelon Form 4. each leading entry in each nonzero row is a 1 5. each leading 1 is the only nonzer...

If the row reduced echelon form of A involves free variables, then the system Ax = b will have infinitely many solutions correct answers FALSE if the system is consistent, and has free variables, it has infinitely many solutions if the system is inconsistent, and has free variables, its does not have infinitely many solutions Every homogeneous linear system is consistent correct answers TRUE every homogenous linear system has zero vectors as the solution An nxn matrix A is nonsign...

Augmented Matrix correct answers a coefficient matrix with an extra column containing the constant terms Consistent system correct answers a system of equations or inequalities that has at least one solution Is the statement "Every elementary row operation is reversible" true or false? correct answers True, because replacement, interchanging, and scaling are all reversible. Is the statement "A 5×6 matrix has six rows" true or false? correct answers False, because a 5×6 matri...

A rectangular matrix is in echelon form if it has the following 3 properties: - Correct Answer-All nonzero rows are above any rows of all zeros; each leading entry of a row is in a column to the right of the leading entry of the row above it; all entries in a column below a leading entry are zeros. leading entry - Correct Answer-leftmost nonzero entry in a nonzero row If a matrix in echelon form satisfies the following additional conditions, then it is in reduced echelon form - Correct Ans...

Elementary Linear Algebra Exam with Answers ordered n-tuple - Answer-a solution of a system of linear equations with n unknowns can be written as (s₁ , s₂ ... sn) or and ordered n-tuple consistent (linear system) - Answer-has at least one solution (1 or ∞ solutions) (no 2 since its linear) inconsistent: no solution augmented matrix - Answer-includes solutions elementary row operations - Answer-1. multiply an equation by a non-zero constant 2. add/subtract a multiple of ano...

MAT1503 Linear Algebra With Complete Solutions Download To Score Distinction homogeneous linear equations - x₁ − 2x₂ − 3x₃ + x₄ = 0 solution of a linear system - The element is a solution of each equation solution set (general solution) - All solutions of a linear system with the number sequence as the elements ordered n-tuple - A linear solution written as (a₁, a₂, ... , a) ordered pair - ordered n-tuple if n = 2 ordered triple - ordered n-tuple if n = 3 co...

If the row reduced echelon form of A involves free variables, then the system Ax = b will have infinitely many solutions correct answers FALSE if the system is consistent, and has free variables, it has infinitely many solutions if the system is inconsistent, and has free variables, its does not have infinitely many solutions Every homogeneous linear system is consistent correct answers TRUE every homogenous linear system has zero vectors as the solution An nxn matrix A is nonsign...

What is a matrix of coefficients? Correct Answer The matrix formed of all the coefficients of one or more sums of variables with coefficients. What is an augmented matrix? Correct Answer The matrix formed of all the coefficients and values of one or more linear equations. What is row echelon form? Correct Answer When each leading entry is to the right of those above it, and any rows of zeros are at the bottom. What is reduced row echelon form? Correct Answer When all leading entries are...

If x1 maximizes a quadratic form, subject to the constraint ||x1||=1, then - so does -x1 If A= A^T x != y, Ax = 3x, and Ay = -y, then - x^Ty = 0 S = {x exists in R^3 | x1 + x2 + x3 = 1}, then - is not a subspace of R^3 If U is an echelon form of matrix A, then - Col(U) != Col(A) Row operations on a nxn matrix do change - its eigenvalues. IF A exists in R^nxn and x and y are vectors in R^n, then Ax * Ay = - x^T(A^T)Ay If the eigenvalues of a 3x3 matrix A are 1,2,4 and A = PBP^-1 for 3x3 mat...