Read the following definitions carefully, and then answer the questions below. Note that one of the definitions appears on Tutorial Worksheet 1, so you should make sure to go to tutorial this week to make sure you are prepared for this assignment! 2 We define a matrix to be ephemeral if the number of non-zero entries is less than or equal to the number of rows or columns, whichever is smaller. ie. if m is the number of rows, and n is the number of columns, then the number of non-zero entries is at most min(m, n). Similarly, a matrix is called solid if the number of entries that are equal to 0 is less than or equal to the number of rows or variables, whichever is smaller. ie. if m is the number of rows, and n is the number of columns, then the number of entries equal to zero is at most min(m,n). you continue, you may wish to explore this definition by creating some examples of ephemeral or solid matrices. Before For each of the following questioms, if the answer is "yes", create such a matrix and explain why it has (or doesn't have) the desired properties; if the answer is "no", give an explanation for why. 4.1 Can a 2 × 2 matrix be both ephemeral and solid? 4.2 Can a 2 x 2 matrix be neither ephemeral nor solid? 4.3 Can a matrix with at least three rows and at least three columns be both ephemeral and solid? 4.4 Can a matrix with at least three rows and ạt least three columns be neither ephemeral nor solid?
Read the following definitions carefully, and then answer the questions below. Note that one of the definitions appears on Tutorial Worksheet 1, so you should make sure to go to tutorial this week to make sure you are prepared for this assignment! 2 We define a matrix to be ephemeral if the number of non-zero entries is less than or equal to the number of rows or columns, whichever is smaller. ie. if m is the number of rows, and n is the number of columns, then the number of non-zero entries is at most min(m, n). Similarly, a matrix is called solid if the number of entries that are equal to 0 is less than or equal to the number of rows or variables, whichever is smaller. ie. if m is the number of rows, and n is the number of columns, then the number of entries equal to zero is at most min(m,n). you continue, you may wish to explore this definition by creating some examples of ephemeral or solid matrices. Before For each of the following questioms, if the answer is "yes", create such a matrix and explain why it has (or doesn't have) the desired properties; if the answer is "no", give an explanation for why. 4.1 Can a 2 × 2 matrix be both ephemeral and solid? 4.2 Can a 2 x 2 matrix be neither ephemeral nor solid? 4.3 Can a matrix with at least three rows and at least three columns be both ephemeral and solid? 4.4 Can a matrix with at least three rows and ạt least three columns be neither ephemeral nor solid?
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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Transcribed Image Text:4
Read the following definitions carefully, and then answer the questions below.
Note that one of the definitions appears on Tutorial Worksheet 1, so you should make sure
go to tutorial this week to make sure you are prepared for this assignment!
to
2
We define a matrix to be ephemeral if the number of non-zero entries is less
than or equal to the number of rows or columns, whichever is smaller. ie. if m is the
number of rows, and n is the number of columns, then the number of non-zero entries is at most min(m,n).
Similarly, a matrix is called solid if the number of entries that are equal to 0 is
less than or equal to the number of rows or variables, whichever is smaller. ie. if m
is the number of rows, and n is the number of columns, then the number of entries equal to zero is at most min(m,n).
Before you continue, you may wish to explore this definition by creating some
examples of ephemeral or solid matrices.
For each of the following questions, if the answer is "yes", create such a matrix and
explain why it has (or doesn't have) the desired properties; if the answer is "no", give an
explanation for why.
4.1 Can a 2 x 2 matrix be both ephemeral and solid?
4.2 Can a 2 x 2 matrix be neither ephemeral nor solid?
4.3 Can a matrix with at least three rows and at least three columns be both ephemeral
and solid?
4.4 Can a matrix with at least three rows and ht least three columns be neither ephemeral
nor solid?
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