Q46E Given some numbers a,b,c,d, e an... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q46E (page 291)

Given some numbers $a, b, c, d$ , $e$ and $f$ such that $d e t [\begin{matrix} a & 1 & d \\ b & 1 & e \\ c & 1 & f \end{matrix}] = 7$ and role="math" localid="1660392376197" $d e t [\begin{matrix} a & 1 & d \\ b & 2 & e \\ c & 3 & f \end{matrix}] = 11$ ,
a. Find $d e t [\begin{matrix} a & 3 & d \\ b & 3 & e \\ c & 3 & f \end{matrix}]$
b. Find $d e t [\begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix}]$

Short Answer

Expert verified

Therefore,

a) $|\begin{matrix} a & 3 & d \\ b & 3 & 3 \\ c & 3 & f \end{matrix}| = 21$

b) $|\begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix}| = 29$

Step by step solution

Step by Step solution: Step 1: 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.

Given

Given matrix,

$d e t [\begin{matrix} a & 1 & d \\ b & 1 & e \\ c & 1 & f \end{matrix}] = 7$

$d e t [\begin{matrix} a & 1 & d \\ b & 2 & e \\ c & 3 & f \end{matrix}] = 11$

(a)Step 3: To find det[a3db3ec3f]

To find $d e t [\begin{matrix} a & 3 & d \\ b & 3 & e \\ c & 3 & f \end{matrix}]$

Let,

$|\begin{matrix} a & 3 & d \\ b & 3 & 3 \\ c & 3 & f \end{matrix}| = 3 . |\begin{matrix} a & 1 & d \\ b & 1 & e \\ c & 1 & f \end{matrix}| |\begin{matrix} a & 3 & d \\ b & 3 & 3 \\ c & 3 & f \end{matrix}| = 3.7 |\begin{matrix} a & 3 & d \\ b & 3 & 3 \\ c & 3 & f \end{matrix}| = 21$

(b)Step 4: To find det|a3db5ec7f|

To find $d e t | \begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix} |$

Let,

$| \begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix} | = 2 | \begin{matrix} a & 1 & d \\ b & 2 & e \\ c & 3 & f \end{matrix} | + | \begin{matrix} a & 1 & d \\ b & 1 & e \\ c & 1 & f \end{matrix} | | \begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix} | = 2.11 + 7 | \begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix} | = 29$

Therefore,

a) $| \begin{matrix} a & 3 & d \\ b & 3 & 3 \\ c & 3 & f \end{matrix} | = 21$

b) $| \begin{matrix} a & 3 & d \\ b & 5 & e \\ c & 7 & f \end{matrix} | = 29$

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Short Answer

Step by step solution

Step by Step solution: Step 1: Definition

Given

(a)Step 3: To find det[a3db3ec3f]

(b)Step 4: To find det|a3db5ec7f|

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91影视

Given some numbers a,b,c,d, e and f such that det[a1db1ec1f]=7 and role="math" localid="1660392376197" det[a1db2ec3f]=11,a. Find det[a3db3ec3f]b. Finddet[a3db5ec7f]

Short Answer

Step by step solution

Step by Step solution: Step 1: Definition

Given

(a)Step 3: To find det[a3db3ec3f]

(b)Step 4: To find det|a3db5ec7f|

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.