A1 A2A3 A4The block matrix A =when A1, A2, A4 are n x n matrices and Az is n x n zero matrix, thenA-1 exists if:O a. A1 & A, are invertible matricesO b. A2&A, are invertible matricesO c. A, & A, are invertible matricesO d. A2 is invertible If A? is a zero matrix, then AA = 0 is:O a. Not possible unless A is a zero matrixO b. not possible at allO C. possible only when A is invertibleO d. possible only when A is symmetric

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A1 A2 A3 A4 The block matrix A = when A1, A2, A4 are n x n matrices and Az is n x n zero matrix, then A-1 exists if: O a. A1 & A, are invertible matrices O b. A2& A, are invertible matrices O c. A, &A2 are invertible matrices O d. A2 is invertible

A1 A2 A3 A4 The block matrix A = when A1, A2, A4 are n x n matrices and Az is n x n zero matrix, then A-1 exists if: O a. A1 & A, are invertible matrices O b. A2& A, are invertible matrices O c. A, &A2 are invertible matrices O d. A2 is invertible

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

A1 A2
A3 A4
The block matrix A =
when A1, A2, A4 are n x n matrices and Az is n x n zero matrix, then
A-1 exists if:
O a. A1 & A, are invertible matrices
O b. A2&A, are invertible matrices
O c. A, & A, are invertible matrices
O d. A2 is invertible

If A? is a zero matrix, then AA = 0 is:
O a. Not possible unless A is a zero matrix
O b. not possible at all
O C. possible only when A is invertible
O d. possible only when A is symmetric

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