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Chapter 1: Q11E (page 35)

(Compute the dot products in Exercises 10 through 12

if the products are defined)

11.

[1997][666]

Short Answer

Expert verified

The dot product of 1997666is not defined.

Step by step solution

01

Step 1:

No steps as the dot product does not exist.

For the first matrix 1997

锘縏he number of columns

m=4

锘縁or the second matrix, 666锘�

The number of rows

n=3

锘縒e can see thatm鈮�n.

Hence, dot product is not possible.

02

Final answer:

The dot product of 1997666is not defined

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Most popular questions from this chapter

a. Find(234567)+(75310-1)

b. Find9(1-12345)

Consider a positive definite quadratic form q onRnwith symmetric matrix. We know that there exists an orthonormal eigenbasis for v鈫�1,...,v鈫�nfor A, with associated positive eigenvalues 位1,...,位n. Now consider the orthogonal Eigen basis w鈫�1,鈥�,w鈫�n, where w鈫�1=1位v鈫�1.

Show that q(c1w鈫�1+......+cnw鈫�n)=cn2.

Let A be a 4 脳 3 matrix, and letb鈫�and c鈫� be two vectors in 鈩�4. We are told that the systemrole="math" localid="1659341825668" Ax鈫�=b鈫� has a unique solution. What can you say about the number of solutions of the systemAx鈫�=c鈫� ?

In Exercises 1 through 12, find all solutions of the equations with paper and pencil using Gauss鈥揓ordan elimination. Show all your work.

|x1-7x2+x5=3x3-2x5=2x4+x5=1|

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|4x1+3x2-2x3-x4=45x1+4x2-3x3-x4=4-2x1-2x2-x3-2x4=-311x1+6x2+4x3-x4=11|
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