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Chapter 3: Q5P (page 112)

In Problems 1 to 5, all lines are in the $(x, y)$ plane.
5. Write, in parametric form, the equation of the $y$ axis.

Short Answer

Expert verified

The parametric form of the equation of $y$ - axis is $y = b t$ .

Step by step solution

01

Concept of parametric form

To find the parametric form of $y$ axis in equation $y = x + b t$

In $y$ axis $x = 0$ .

02

Determine the parametric form

Consider the equation of $y -$ axis is $x = 0$ .

The parametric form of $y$ - axis is $y = x + b t$

$y = 0 + b t y = b t$

Hence, the parametric form of the equation of $y$ -axis is $y = b t$ .

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Most popular questions from this chapter

Verify the details as indicated in diagonalizing H in (11.29).

Find AB,BA,A+B,A-B, $A^{2}$ , $B^{2}$ ,5-A,3-B. Observe that $AB \neq BA$ .Show that $(A - B) (A + B) \neq (A + B) (A - B) \neq A^{2} - B^{2}$ . Show that $\det (AB) = \det (BA) = (detA) (detB)$ , but that $\det (A + B) \neq detA + detB .$ Show that $\det (5 A) \neq 5 detA$ and find n so that localid="1658983435079" $\det (5 A) = 5^{n} detA .$ Find similar results for $\det (3 B)$ . 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.

localid="1658983077106" $A = (\begin{matrix} 2 & 5 \\ - 1 & 3 \end{matrix}), B = (\begin{matrix} - 1 & 4 \\ 0 & 2 \end{matrix})$

Show that the given lines intersect and find the acute angle between them.

$r = (5, - 2, 0) + (1, - 1 - 1) t_{1} and r = (4, - 4, - 1) + (0, 3, 2) t_{2}$

Question: 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.

$(\begin{matrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{matrix})$

The diagonals of a rhombus (four-sided figure with all sides of equal length) are perpendicular and bisect each other.

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