Problem 1. Determine if each of the following statements is true or false. Supporting work is not required. Let T : R* → R³ be a surjective linear transformation. Let A be the matrix corresponding to T. Then rankA = 3. True False There exists a 4 x 5 matrix A satisfying rankA = nullityA. True False Let A be a matrix, and B,C be two (arbitrary) echelon forms of A. Then det B = det C. %3D True False | Let A be a n x n matrix such that A2021 = A. If v is an eigenvector of A, then v is an eigenvector of A2021. True False Let A be a n x n matrix. Suppose that A has n distinct eigenvalues, then A is diagonalizable. True False

Problem 1. Determine if each of the following statements is true or false. Supporting work is not required. Let T : R* → R³ be a surjective linear transformation. Let A be the matrix corresponding to T. Then rankA = 3. True False There exists a 4 x 5 matrix A satisfying rankA = nullityA. True False Let A be a matrix, and B,C be two (arbitrary) echelon forms of A. Then det B = det C. %3D True False | Let A be a n x n matrix such that A2021 = A. If v is an eigenvector of A, then v is an eigenvector of A2021. True False Let A be a n x n matrix. Suppose that A has n distinct eigenvalues, then A is diagonalizable. True False

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

Problem 1.
Determine if each of the following statements is true or false.
Supporting work is not required.
Let T : R' → R3 be a surjective linear transformation. Let A be the matrix
corresponding to T. Then rankA = 3.
True
False
There exists a 4 × 5 matrix A satisfying rankA = nullity A.
True
False
Let A be a matrix, and B,C be two (arbitrary) echelon forms of A. Then
det B = det C.
True
False
| Let A be a n x n matrix such that A2021
A. If v is an eigenvector of A,
then v is an eigenvector of A2021.
True
False
Let A be a n x n matrix. Suppose that A has n distinct eigenvalues, then A
is diagonalizable.
True
False

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