Calculate the inverse of the following matrix: 1-23M29.-6-1-6||

Given matrix is M=1−2329−6−15−6. We have to find the inverse of the matrix M.…

Answered: 1 -2 3 -6 -1 -6]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Calculate the inverse of the following matrix:

Expert Solution

Step 1

Given matrix is $M = [\begin{matrix} 1 & - 2 & 3 \\ 2 & 9 & - 6 \\ - 1 & 5 & - 6 \end{matrix}]$ .

We have to find the inverse of the matrix $M$ .

$\begin{matrix} \det (M) = 1 (- 54 + 30) - (- 2) (- 12 - 6) + 3 (10 + 9) \\ = 1 (- 24) + 2 (- 18) + 3 (19) \\ = - 24 - 36 + 57 \\ = - 3 \end{matrix}$

Hence, $\det (M) = - 3$

Now, we will find the cofactors of the matrix $M$ .

$a_{11} = |\begin{matrix} 9 & - 6 \\ 5 & - 6 \end{matrix}| = - 54 + 30 = - 24$

$a_{12} = - |\begin{matrix} 2 & - 6 \\ - 1 & - 6 \end{matrix}| = - (- 12 - 6) = 18$

$a_{13} = |\begin{matrix} 2 & 9 \\ - 1 & 5 \end{matrix}| = 10 + 9 = 19$

$a_{21} = - |\begin{matrix} - 2 & 3 \\ 5 & - 6 \end{matrix}| = - (12 - 15) = 3$

$a_{22} = |\begin{matrix} 1 & 3 \\ - 1 & - 6 \end{matrix}| = - 6 + 3 = - 3$

$a_{23} = - |\begin{matrix} 1 & - 2 \\ - 1 & 5 \end{matrix}| = - (5 - 2) = - 3$

$a_{31} = |\begin{matrix} - 2 & 3 \\ 9 & - 6 \end{matrix}| = 12 - 27 = - 15$

$a_{32} = - |\begin{matrix} 1 & 3 \\ 2 & - 6 \end{matrix}| = - (- 6 - 6) = 12$

$a_{33} = |\begin{matrix} 1 & - 2 \\ 2 & 9 \end{matrix}| = 9 + 4 = 13$

Hence, the cofactor matrix, is given by

$B = [\begin{matrix} - 24 & 18 & 19 \\ 3 & - 3 & - 3 \\ - 15 & 12 & 13 \end{matrix}]$

Now, $a d j (M) = B^{T} = [\begin{matrix} - 24 & 3 & - 15 \\ 18 & - 3 & 12 \\ 19 & - 3 & 13 \end{matrix}]$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS