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Chapter 3: Q22P (page 105)

Square (A+B); interpret your result geometrically. Hint: Your answer is a law which you learned in trigonometry.

Short Answer

Expert verified

The law of cosine |A|2+|B|2+2A脳B.

Step by step solution

01

Concept and formula used

Using the formula,

(A+B)2=(A+B)脳(A+B)

The Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

02

Step 2: Using the trigonometric law

Squaring (A+B),

(A+B)2=(A+B)脳(A+B)=|A|2+A脳B+B脳A+|B|2=|A|2+2A脳B+|B|2

This is law of cosine.

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Most popular questions from this chapter

Find the Eigen values and Eigen vectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.

(230320001)

In (9.1) we have defined the adjoint of a matrix as the transpose conjugate. This is the usual definition except in algebra where the adjoint is defined as the transposed matrix of cofactors [see (6.13)]. Show that the two definitions are the same for a unitary matrix with determinant=+1

Note in Section 6 [see (6.15)] that, for the given matrix A, we found A2=-I, so it was easy to find all the powers of A. It is not usually this easy to find high powers of a matrix directly. Try it for the square matrix Min equation (11.1). Then use the method outlined in Problem 57 to findM4,M10.eM.

Draw diagrams and prove (4.1).

In Problems8to15,use (8.5) to show that the given functions are linearly independent.

1,x2,x4,x6
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