Q 6.2-58E ... [FREE SOLUTION]

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Linear Algebra With Applications

Otto Bretscher

$Math Studyset Vaia Explanations$ Math

5th Edition · 442 pages

ISBN: 9780321796974

Chapter 6: Q 6.2-58E (page 292)

Short Answer

Expert verified

Therefore, the matrix M is given by, .

Step by step solution

Matrix Definition

Matrix is aset of numbers arranged inrowsandcolumnsso as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be a “m by n” matrix, written “ m×n.”

Given

Given linear transformation,

To find Matrix M.

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Most popular questions from this chapter

If $A$ and $B$ are invertible $n \times n$ matrices, and if $A$ is similar to $B$ , is $adj (A)$ necessarily similar to $adj (B)$ ?

Consider two distinct real numbers, a and b. We define the function

$f (t) = d e t [\begin{matrix} 1 & 1 & 1 \\ a & b & t \\ a^{2} & b^{2} & t^{2} \end{matrix}]$

a. Show that $f (t)$ is a quadratic function. What is the coefficient of $t^{2}$ ?
b. Explain why $f (a) = f (b) = 0$ . Conclude that $f (t) = k (t - a) (t - b)$ , for some constant k. Find k, using your work in part (a).
c. For which values of tis the matrix invertible?

Question:A basis $\vec{v_{1}}, \vec{v_{2}}, \vec{v_{3}}$ of $ℝ^{3}$ is called positively oriented if $\vec{v_{1}}$ encloses an acute angle with $\vec{v_{2}} \times \vec{v_{3}}$ . Illustrate this definition with a sketch. Show that the basis is positively oriented if (and only if) $d e t [\vec{v_{1}}, \vec{v_{2}}, \vec{v_{3}}]$ is positive.

Find the 3-volume of the 3-parallelepiped defined by the vectors

$[\begin{matrix} 1 \\ 0 \\ 0 \\ 0 \end{matrix}], [\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}], [\begin{matrix} 1 \\ 2 \\ 3 \\ 4 \end{matrix}]$ .

$d e t (A + B) = d e t A + d e t B$ for all $5 \times 5$ matricesA andB.

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Short Answer

Step by step solution

Matrix Definition

Given

To find Matrix M.

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Most popular questions from this chapter

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