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Chapter 3: 2P (page 88)

As in Problem 1, write out in detail in terms of equations like (2.6) for two equations in four unknowns; for four equations in two unknowns.

Short Answer

Expert verified

The form iswhich can be written as:

The form is

Step by step solution

01

Concept of matrix

Amatrixis just a rectangular array of quantities, usually enclosed in large parentheses, such as:

02

Write the terms of Mij,xj and ki for two equations

We can write the equations for two equations in four unknowns as:

We can write this in detail as:

03

Write the terms of Mij,x j  , and ki for four equations

We can write the equation for four equations in two unknowns as:

We can write this in detail as:

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Most popular questions from this chapter

Find the angles between (a) the space diagonals of a cube; (b) a space diagonal and an edge; (c) a space diagonal and a diagonal of a face.

For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using.

3.

Find the rank of each of the following matrices.

(112246325)

Find AB, BA , A+B , A-B , A2, B2,5.A,3,B . Observe that AB鈮�BA. Show that (A-B)(A+B)鈮�(A+B)(A-B)鈮�A2-B2. Show that det(AB)=det(BA)=(detA)(detB), but that det(A+B)鈮�detA+detB. Show that det(5A)鈮�5detA and find n so that det(5A)=5ndetA. Find similar results for det(3B). Remember that the point of doing these simple problems by hand is to learn how to manipulate determinants and matrices correctly. Check your answers by computer.

role="math" localid="1658986967380" A=(1023-10051),B=(1100213-10)

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

(-121230103)
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