Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra1st Quiz, SolutionFebruary 15, 2005Problem 1Given the following system of equations:x-3y+z= 1x+y+ 2z= 14find all solutions using Gauss-Jordan elimination procedure. Is this an exampleof consistent system? Why?Solution1-31112114Row(II)-Row(I):1-31041113Row(II)÷4:1-3101141134Row (I)+ Row (II)×3:107401144341341
Therefore, the answer is:x=434-74zy=134-14zz=any real numberOf course, consistent system and has infinite solutions.Problem 2Find the rank of the following matrix10112-111000111110112Solution10112-111000111110112+(I)-(I)then:10112012120111100000-(II)then:101120121200-10-100000×(-1)then:10112012120010100000-(III)-(2×(III))2
then:10011010100010100000Here, we see, the reduced row-echelon form has 3 leading 1’s, therefore, the rankis 3.

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Term
Spring
Professor
CONSANI
Tags
Linear Algebra, Algebra, Equations, Gauss Jordan Elimination, Gaussian Elimination, British B class submarine, B type proanthocyanidin, B2 B3 B4

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