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Get Full Access to Linear Algebra: A Geometric Approach - 2 Edition - Chapter 5.2 - Problem 16
Get Full Access to Linear Algebra: A Geometric Approach - 2 Edition - Chapter 5.2 - Problem 16

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# In this problem, let D(x, y) denote the determinant of the 2 2 matrix with rows x and y ISBN: 9781429215213 438

## Solution for problem 16 Chapter 5.2

Linear Algebra: A Geometric Approach | 2nd Edition

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Problem 16

In this problem, let D(x, y) denote the determinant of the 2 2 matrix with rows x and y. Assume the vectors v1, v2, v3 R2 are pairwise linearly independent. a. Prove that D(v2, v3)v1 + D(v3, v1)v2 + D(v1, v2)v3 = 0. (Hint: Write v1 as a linear combination of v2 and v3 and use Cramers Rule to solve for the coefficients.) b. Now suppose a1, a2, a3 R2 and for i = 1, 2, 3, let _i be the line in the plane passing through ai with direction vector vi . Prove that the three lines have a point in common if and only if D(a1, v1)D(v2, v3) + D(a2, v2)D(v3, v1) + D(a3, v3)D(v1, v2) = 0. (Hint: Use Cramers Rule to get an equation that says that the point of intersection of _1 and _2 lies on _3.)

Step-by-Step Solution:
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Calculus 1 Chapter 2, Section 2 – Intro to Limits (cont.) and Their Properties Prior to this, were learning how to solve limits as x approaches a number analytically with use of algebra, but now we are going to look at how to solve a limit using a table method. Don’t worryit is not anything hard, it concludesofmaking a table andwriting down close numbers to the leftandrightofthe limitandpluggingthosevaluesto findvaluesthatdrawclosetothelimit.Thisapretty simple method to follow. Let’s look at an example which we can solve for the limit using the table method: Ex.1: − 7 + 12 () = lim = →3 − 3 First, we mus

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##### ISBN: 9781429215213

The answer to “In this problem, let D(x, y) denote the determinant of the 2 2 matrix with rows x and y. Assume the vectors v1, v2, v3 R2 are pairwise linearly independent. a. Prove that D(v2, v3)v1 + D(v3, v1)v2 + D(v1, v2)v3 = 0. (Hint: Write v1 as a linear combination of v2 and v3 and use Cramers Rule to solve for the coefficients.) b. Now suppose a1, a2, a3 R2 and for i = 1, 2, 3, let _i be the line in the plane passing through ai with direction vector vi . Prove that the three lines have a point in common if and only if D(a1, v1)D(v2, v3) + D(a2, v2)D(v3, v1) + D(a3, v3)D(v1, v2) = 0. (Hint: Use Cramers Rule to get an equation that says that the point of intersection of _1 and _2 lies on _3.)” is broken down into a number of easy to follow steps, and 142 words. Linear Algebra: A Geometric Approach was written by and is associated to the ISBN: 9781429215213. This full solution covers the following key subjects: . This expansive textbook survival guide covers 31 chapters, and 547 solutions. Since the solution to 16 from 5.2 chapter was answered, more than 218 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Linear Algebra: A Geometric Approach, edition: 2. The full step-by-step solution to problem: 16 from chapter: 5.2 was answered by , our top Math solution expert on 03/15/18, 05:30PM.

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