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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q 6.2-64E (page 293)

Short Answer

Expert verified

Therefore, the expression of L_n is given by,

Step by step solution

Definition

A determinant is a unique number associated with asquare matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

To find the formula expressing in Ln terms

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Most popular questions from this chapter

There exists a real $3 脳 3$ matrix $A$ such that $A^{2} = - l_{3}$ .

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

If all the entries of a $7 脳 7$ matrix A are 7, then $d e t A$ must be $7^{7}$ .

If all the columns of a square matrixAare unit vectors, then the determinant ofAmust be less than or equal to 1.

There exists a $4 脳 4$ matrix whose entries are all 1or -1 , and such that $d e t A = 16$ .

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Short Answer

Step by step solution

Definition

To find the formula expressing in Ln terms

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