Q 31E Question:聽For which values of t... [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 2: Q 31E (page 98)

Question:For which values of the constants a, band cis the following matrix invertible?
$(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$

Short Answer

Expert verified

The matrix, $(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$ is never invertible.

Step by step solution

Consider the matrix

Consider the matrix.

$(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$

The matrix is said to be invertible if and only if the determinant of the matrix is nonzero.

Compute the determinant of the matrix

The determinant of the matrix is,

$\begin{matrix} \det (\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix}) = 0 鈰� \det (\begin{matrix} 0 & c \\ 鈭� c & 0 \end{matrix}) 鈭� a \det (\begin{matrix} 鈭� a & c \\ 鈭� b & 0 \end{matrix}) + b \det (\begin{matrix} 鈭� a & 0 \\ 鈭� b & 鈭� c \end{matrix}) \\ = 0 鈰� 鈥� c^{2} 鈭� a b c + b a c \\ = 0 \end{matrix}$

As the determinant of the matrix is zero, hence, the matrix, $(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$ is not invertible.

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91影视

Question:For which values of the constants a, band cis the following matrix invertible?
$(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$

Short Answer

Step by step solution

Consider the matrix

Compute the determinant of the matrix

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91影视

Question:For which values of the constants a, band cis the following matrix invertible?(0ab鈭�a0c鈭�b鈭�c0)

Short Answer

Step by step solution

Consider the matrix

Compute the determinant of the matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Logic and Functions

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Question:For which values of the constants a, band cis the following matrix invertible?
$(\begin{matrix} 0 & a & b \\ 鈭� a & 0 & c \\ 鈭� b & 鈭� c & 0 \end{matrix})$