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Chapter 1: Q10E (page 35)

(Compute the dot products in Exercises 10 through 12

if the products are defined)

10.

[123],[1-21]

Short Answer

Expert verified

The dot product of 123,1-21is not defined.

Step by step solution

01

Step 1:

No steps as the dot product is not possible.

For the first matrix 123

锘縏he number of rows

m=3

锘縁or the second matrix1-21

The number of columns

n=1

锘縒e can see thatm鈮�n.

Hence, dot product is not possible.

02

Final answer:

The dot product of 123,1-21is not defined.

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Most popular questions from this chapter

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.

|x2+2x4+3x5=04x4+8x5=0|

Consider a solutionx1鈫�of the linear systemAx鈫�=b鈫�. Justify the facts stated in parts (a) and (b):

a. Ifx鈫�his a solution of the systemAx鈫�=0鈫�, thenx1鈫�+xh鈫� is a solution of the systemA=x鈫�=b鈫�.

b. Ifx2鈫�is another solution of the systemAx鈫�=b鈫�, thenx1鈫�+xh鈫�is a solution of the system Ax鈫�+0鈫�.

c. Now suppose A is a2脳2matrix. A solution vectorx1鈫�of the systemAx鈫�+b鈫�is shown in the accompanying figure. We are told that the solutions of the systemAx鈫�=0鈫�form the line shown in the sketch. Draw the line consisting of all solutions of the systemAx鈫�=b鈫�.

If you are puzzled by the generality of this problem, think about an example first:

A=(1鈥呪赌呪赌呪赌�23鈥呪赌呪赌呪赌�6),b鈫�=[39]andx1鈫�=[11]

Balancing a chemical reaction. Consider the chemical reaction

aNO2+bH2O鈫�cHNO2+dHNO3,

where a, b, c, and d are unknown positive integers. The reaction must be balanced; that is, the number of atoms of each element must be the same before and after the reaction. For example, because the number of oxygen atoms must remain the same,

2a+b=2c+3d.

While there are many possible values for a,b,c and d that balance the reaction, it is customary to use the smallest possible positive integers. Balance this reaction.

In Exercises 57 through 61, consider a quadratic form q on R3with symmetric matrix A, with the given properties. In each case, describe the level surface q(x鈬赌)=1geometrically.

60. qis indefinite and det A>0.

Compute the productsAx鈫� in Exercises 16 through 19 using paper and pencil (if the products are defined).

18. [123456][12]
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