3. 4. Consider the matrixA: =3 301 2230(1) Compute the determinant of A, i.e., det(A) and the state whether the matrix issingular or nonsingular.(2) Compute the adjoint of A, i.e., adj (A). If A is nonsingular, compute A-¹. Writeout Rank(A).

Given, So, matrix A is nonsingular.

Answered: 3. 4. Consider the matrix A = 3 0 0 3 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

3. 4. Consider the matrix
A: =
3 3
01 2
23
0
(1) Compute the determinant of A, i.e., det(A) and the state whether the matrix is
singular or nonsingular.
(2) Compute the adjoint of A, i.e., adj (A). If A is nonsingular, compute A-¹. Write
out Rank(A).

Expert Solution

Step 1: Question (1)

Given, $A equals open parentheses table row 3 3 1 row 0 1 2 row 0 2 3 end table close parentheses$

$d e t left parenthesis A right parenthesis equals 3 open vertical bar table row 1 2 row 2 3 end table close vertical bar minus 3 open vertical bar table row 0 2 row 0 3 end table close vertical bar plus 1 open vertical bar table row 0 1 row 0 2 end table close vertical bar space space space space space space space space space equals 3 left parenthesis 3 minus 4 right parenthesis minus 3 left parenthesis 0 minus 0 right parenthesis plus 1 left parenthesis 0 minus 0 right parenthesis space space space space space space space space space equals negative 3 space space space space space space space space space not equal to 0$

$d e t A equals negative 3 not equal to 0$

So, matrix A is nonsingular.