You are watching: Reducing a matrix to echelon form is called the forward phase of the row reduction process

Linear Algebra and also Its Applications, 5th Edition

Authors: David C. Lay, Steven R. Lay, Judi J. McDonald

ISBN-13: 978-0321982384

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See our equipment for question 22E from chapter 1.2 indigenous Lay's linear Algebra and Its Applications, fifth Edition.

**Chapter:**1.11.21.31.41.51.61.71.81.91.101.SE2.12.22.32.42.52.62.72.82.92.SE3.13.23.33.SE4.14.24.34.44.54.64.74.84.94.SE5.15.25.35.45.55.65.75.85.SE6.16.26.36.46.56.66.76.86.SE7.17.27.37.47.57.SE8.18.28.38.48.58.6

**Problem:**1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E

a. The echelon kind of a matrix is unique.b. The pivot location in a matrix rely on whether heat interchanges are used in the heat reduction process.c. Reducing a matrix to echelon form is called

Step 1 that 2

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**Given Information**We are given with part statements, we need to prove whether they space true or false

**Step-1: (a)**Statement: The echelon kind of a procession is distinctive The statement is False! The echelon type must satisfy complying with properties: (1) all nonzero rows are over the zero rows; (2) all entries listed below the leasing entrance in a tower is zero; (3)Leading entrance of a heat is ideal of the leasing entrance of the over row for a matrix there deserve to be plenty of forms the can accomplish these properties. However, the row-reduced echelon form is unique, that has actually all pivot facets equal to 1. FALSE

**Step-2: (b)**Statement: The pivot location in a matrix count on whether heat interchanges are offered in the row diminished processThe explain is False! By organize 1, each matrix is row equivalent to one and also only one decreased echelon matrix. FALSE

**Step-3: (c)**Statement: reducing a matrix to echelon kind is referred to as the forward step of the heat reduction process.The statement is yes, really! As declared in example-3 that the textbook, the forward phase has 4 steps: Step-1: start with the leftmost nonzero column. This is a pivot column. The pivot place is at the top.Step-2: choose a nonzero entry in the pivot obelisk as a pivot. If necessary, interchange rows to move this entry right into the pivot position.Step-3: usage row instead of operations to develop zeros in all positions below the pivotStep-4: cover (or ignore) the row containing the pivot position and cover every rows, if any, over it. Apply steps 1–3 to the submatrix the remains. Repeat the process until there are no much more nonzero rows to change TRUE

**Step-4: (d)**Statement: anytime a mechanism has totally free variables, the solution set contains many solutions.. The explain is FALSE! There can be instances when the device has an ext variables then number of equations yet the system has no solution. An example of together augmented type is presented below:

**Step-5: (e)**Statement: A general solution of a system is an explicit summary of all options of the system.The statement is yes, really! A basic solution the a system is indistinguishable to the parametric kind of solution. We compose the soltuion in regards to a parameter (free variable(s)). For various values the parameter, we obtain different solution. So The general solution explains all solution of the system. TRUE