Row echelon form - Study guides, Class notes & Summaries

Elementary row operations Correct Answer 1. (Replacement) Replace one row by the sum of itself and a multiple of another row. 2. (Interchange) Interchange two rows. 3. (Scaling) Multiply all entries in a row by a nonzero constant. X1+x2+x3=2 X2+x3=9 0=-1 This set has ______ solutions and is _________ Correct Answer No solutions, is empty Consistant system Correct Answer a system of equations or inequalities that has at least one solution. The system is consistent because the system ca...

MATH 225 Final Exam Questions with complete solutions | Latest 2023/2024 Augmented Matrix --a coefficient matrix with an extra column containing the constant terms Consistent system --a system of equations or inequalities that has at least one solution Is the statement "Every elementary row operation is reversible" true or false? --True, because replacement, interchanging, and scaling are all reversible. Is the statement "A 5×6 matrix has six rows" true or false? --False, because a ...

1.2 Row Reduction and Echelon Forms Exam with Questions and Answers A rectangular matrix is in echelon form if it has the following 3 properties: 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 ANSWER leftmost nonzero entry in a nonzero row If a matrix in echelon form satisfies the following additional condition...

diagonal matrix square matrix which all non-diagonal entries are 0 diagonal entries can be 0 identity matrix diagonal matrix which all entries along main diagonal is 1, all other entries = 0 can different sized matrices be added? no matrix addition [3|-4] + [-2|8] [1|0] + [-5|-3] = [3+-2|-4+8] [1+-5|0+-3] = [1|4] [-4|-3] scalar refers to real numbers ex_ 3, -5.1, π scalar multiple each entry is multiplied by scalar multiplying mat...

linear equation - Answers-An equation that can be written as a1x1 + a2x2 + ... = b; a1, a2, etc. are real or complex numbers known in advance consistent system - Answers-Has one or infinitely many solutions inconsistent system - Answers-Has no solution leading entry - Answers-Leftmost non-zero entry in a non-zero row Echelon form - Answers-1. All nonzero rows are above any all zero rows; 2. Each leading entry is in a column to the right of the previous leading entry; 3. All entries b...

Finding a parametric description of the solution set of a linear system is the same as solving the system. Is this statement true or​ false? - Answer The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has at least one solution. If one row in an echelon form of an augmented matrix is [ 0 0 0 5 0 ] then the associated linear system is inconsistent. Is this statement true or​ false? - Answer The statement is fals...

Finding a parametric description of the solution set of a linear system is the same as solving the system. Is this statement true or false? - correct answer The statement is false. The solution set of a linear system can only be expressed using a parametric description if the system has at least one solution. If one row in an echelon form of an augmented matrix is [ 0 0 0 5 0 ] then the associated linear system is inconsistent. Is this statement t...

1.2 - Row Reduction and Echelon Form Exam with 100% Correct Answers 2023

row echelon form - correct answer The form of a matrix with the following properties: 1. All nonzero rows are above any rows of all zeros. 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 zeros. reduced row echelon form - correct answer The form of a matrix with the properties of row echelon form as well as: 1. The leading entry in each nonzero row is 1 and 2. Each leading 1 is the only ...