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Chapter 5: Q10E (page 215)

For which value(s) of the constant k are the vectors

u鈫�=[234]andv鈫�[1k1]and perpendicular?

Short Answer

Expert verified

The value of k is -2.

Step by step solution

01

Property of dot product

It is given that the vectors u鈫�=[234],v鈫�=[1k1]are perpendicular. Which implies that, the angles between both the vectors is 蟿蟿/2.

Since, the angle is 蟿蟿/2, so cos(胃)=0.

02

Determine the dot product

As, the dot product will be zero. Then,

u鈫�.v鈫�=0

234.1k1=0

2+k+4=06+3k=03k=-4k=-2

Hence, the vectors are perpendicular and the value ofk is -2 .

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Most popular questions from this chapter

(a) Consider an matrix A such that A螕A=Im. It is necessarily true that? Explain.

(b) Consider an n脳nmatrix A such that ATA=In. Is it necessarily true that AAT=In? Explain.

Consider a linear transformationL from RmtoRn that preserves length. What can you say about the kernel of L? What is the dimension of the image? What can you say about the relationship between n and m? If Ais the matrix of L, What can you say about the columns of A? What isATA? What aboutAAT? Illustrate your answer with an example where m=2and n=3.

Consider a subspace Vof Rnand a vector x鈫� inRn. Let y鈫�=projVx鈫�. What is the relationship between the following quantities?

||y鈫�||2and y鈫�.x鈫�

TRUE OR FALSE? The equation det(AT)=det(A)holds for all 2脳2matrices A.

If A and B are arbitraryn脳n matrices, which of the matrices in Exercise 21 through 26 must be symmetric?

B(A+A螕)B螕.
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