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Chapter 6: Q 6.3-4E (page 305)

Question: Consider the area of the triangle with vertices, .

Express A in terms of

Short Answer

Expert verified

Therefore, the Area of triangle express in terms of is,

Step by step solution

01

Definition. 

Basically, it is equal to half of the Area of the parallelogram.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

A = 1/2 脳 b 脳 h

02

Given. 

Given Matrix,

, and .

03

To find the area of the triangle.

The area of this triangle, whose vertices are,

Is the same as the area of a triangle formed by,

and

So

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Most popular questions from this chapter

For an invertible nxn matrix A, what is the relationship between det (A) and det (A)?

Consider the function F(A)=F[v鈫�w鈫�]=v鈫�脳w鈫�from 鈩�2脳2 to鈩�, the dot product of the column vectors of A.
a. Is Flinear in both columns of A? See Example 6.
b. Is F linear in both rows of A?
c. Is Falternating on the columns of A? See Example 4.

Use Exercise 31 to find

det[1111112345149162518276412511681256625]

Do not use technology.

Show that an nxn matrixAhas at least one nonzero minor if (and only if) rank(A)鈮�n-1.

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.
See all solutions

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