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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 4.2 - Problem 40e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 4.2 - Problem 40e

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# Then H and K are subspaces of . In fact, H and K are

ISBN: 9780321982384 49

## Solution for problem 40E Chapter 4.2

Linear Algebra and Its Applications | 5th Edition

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Problem 40E

Then H and K are subspaces of . In fact, H and K are planes in through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. [Hint: w can be written as To build w, solve the equation

Step-by-Step Solution:

Solution 40 EStep 1 of 4Consider the vectors Suppose that the subspaces and intersect in a line through 0.The objective is to find a nonzero vector w that generates the line.Since and intersect in a line, so w is in both H and K.Therefore, w can be expressed as a linear combination of and also as a linear combination of .Thus, write the vector w as .Therefore, the following equation is obtained:

Step 2 of 4

Step 3 of 4

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