Question

Problem 2. Solve the 3 × 3 linear system $x' = -5x + 4y + 2z$ $y' = 2y + 3z$ $z' = 7z$ x(0) = 2 y(0) = 2 z(0) = 2 The determinant of a 3 × 3 matrix is defined as follows $\det \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = a(ei - hf) - b(di - gf) + c(dh - ge).$

          Problem 2. Solve the 3 × 3 linear system
$x' = -5x + 4y + 2z$
$y' = 2y + 3z$
$z' = 7z$
x(0) = 2
y(0) = 2
z(0) = 2
The determinant of a 3 × 3 matrix is defined as follows
$\det \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} = a(ei - hf) - b(di - gf) + c(dh - ge).$

Problem 2. Solve the 3 × 3 linear system
x' = -5x + 4y + 2z
y' = 2y + 3z
z' = 7z
x(0) = 2
y(0) = 2
z(0) = 2
The determinant of a 3 × 3 matrix is defined as follows
< p m a t r i x >
= a(ei - hf) - b(di - gf) + c(dh - ge).

Added by Monica E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/22/2023

Step 1

Step 1: Write the given system of differential equations in matrix form: \[ \frac{d}{dt} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} -5 & 4 & 2 \\ 0 & 2 & 3 \\ 0 & 0 & 7 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} \] Show more…

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Problem 2 . Solve the 3 imes 3 linear system x^(')=-5x+4y+2z y^(')=2y+3z z^(')=7z x(0)=2 y(0)=2 z(0)=2 The determinant of a 3 imes 3 matrix is defined as follows det([a,b,c],[d,e,f],[g,h,i])=a(ei-hf)-b(di-gf)+c(dh-ge) Problem 2. Solve the 3 x 3 linear system x'=-5x+4y+ 2z y'=2y+3z z'=7z x(0) = 2 y(0) = 2 z(0) = 2 The determinant of a 3 x 3 matrix is defined as follows a b c det d e g h 2 = a(ei - hf) - b(di - gf) + c(dh - ge).