4-020.AConsider the following matrices[1 0 1 1]10 0 211 1 0'00 1 0=B =Note that only the entries of matrix C are in Zg. The other two matrices A and B arematrices with real numbers entries.(a) Find the inverse of all the given matrices, if they are invertible, using Gauss-Jordanmethod?Invertibility of A:Invertibility of B:C = 2 3 2 (Entries of C are from Z9).85Invertibility of C: (b) Write the inverse of the given matrices as the product of elementary matrices (Find asequence of elementary matrices whose product in a correct order is equal to inversematrix).For A:For B:For C:

A matrix if called invertible if we can find its inverse, i.e.

Answered: B = 1002 1 1 1 0 0 0 10 3 [1 3 1] C = 2…

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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Similar questions

Consider the matrix [102] A = 2 1 4 5 5 9 (a) Use elementary row operations to reduce A into the identity matrix I. (b) List all corresponding elementary matrices. (c) Write A-¹ as a product of elementary matrices.
Which of the following statements are always true? (i) Suppose that A and B are nxn matrices. If the matrix AB is invertible then B can be expressed as a product of elementary matrices. (ii) If A and B are invertible matrices then then (BA)x O has only the trivial solution. (iii) If A is an invertible 38 x 38 matrix then the reduced row-echelon form of A' is the identity matrix.
2
Help me with this one please, it's about linear algebra (matrix) Thankyou in advance! Need to review this after.
(-2 4) 3. Matrices A and B are given as 2 3 A=-1 0 4 and B=-1 -1 0 2 2) | 1 1 -1 (a) Find the value of K if AB = KI, where I is an identity matrix. (b) Hence, find matrix C such that C= AB+10/3, where Ig is an 3x3 identity matrix. Page 1 1 PrtScn F8 Home F9 F4 F5 F6
3
А В Let the 4 x 4 matrix M is written as 2 × 2 block matrices in the form M where A, B, D are 2 × 2 matrices and 0 is the 2 × 2 zero matrix. Prove that det(M) det(A) det(D). IE M = ( A where A, B, C, D are 2 × 2 matrices, then can you say det(M) = C D det(A) det(D) – det(B) det(C)? Justify your answer.
False/True: If A,B are invertible n x n matrices, then so is A+B. True False
i -1 2] Find the matrix A if (5A)" =|0 2 2 0 |3 -1 4
Consider the matrices 1 -1 2 -4 -1 A 1 and BA 3 -7 -1 1 4 1 (a) to find A-1. Show that A is non-singular (invertible) and then use the method of cofactors (Ъ) (c) Use part(a) to find the matrix B. Use parts (a) and (b) to calculate det(3A² BT).
(2) Find the examples that satisfy the statement in the given items and show some work how they are correct examples (a) A 4 x 4 matrices A that is not digonalizable. (b) (c) Two matrices A and B that have the same characteristic polynomial but are not similar. Two diagonal matrices D₁ and D₂ that are similar but they are not equal. (d) Two similar matrices A and B such that A is orthogonally digonalizable but B is not orthogonally diagonalizable.
matrix, B is a skew-symmetric matrix, and C = (A + B) ¹(A - B), then prove that (ii) C¹(A-B)C=A-B If A is a symmetric A + B is nonsingular (1) C(A + B)C=A+B (iii) CTAC = A

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