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Math / Linear Algebra and Its Applications 5 / Chapter 4.2 / Problem 40E

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

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

Chapter 4, Problem 40E

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QUESTION:

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

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QUESTION:

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

ANSWER:

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:

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