1. (a) Give an example of a matrix A with rank 3 and nullity 2. Try to give a different example than your classmates. (b) If A is any mxn matrix with rank 3 and nullity 2, what can you say about n? Explain. (c) If A is any matrix mx n with rank 3 and nullity 2, what can you say about m? Explain.
1. (a) Give an example of a matrix A with rank 3 and nullity 2. Try to give a different example than your classmates. (b) If A is any mxn matrix with rank 3 and nullity 2, what can you say about n? Explain. (c) If A is any matrix mx n with rank 3 and nullity 2, what can you say about m? Explain.
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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![1. (a) Give an example of a matrix A with rank 3 and nullity 2. Try to give a different example
than your classmates.
(b) If A is any mx n matrix with rank 3 and nullity 2, what can you say about n? Explain.
(c) If A is any matrix mx n with rank 3 and nullity 2, what can you say about m? Explain.
Un ]
2. Suppose 01, 02,..., Un are vectors in Rm and, as usual, write A = [ 0₁ 02
(a) What can you say about the set of vectors V₁, V2,..., Un if rank(A) = m?
(b) What can you say about the set of vectors V1, V2, ..., Un if rank(A) = n?
(c) What can you say about the set of vectors V1, V2,..., Un if nullity (A) = 0?
(d) What can you say about the set of vectors V₁, V2,..., Un if nullity(A) > 0?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a7e99bb-b9c4-47fa-9081-3b9aeb6b94e4%2F1e38e670-242d-458e-ae7f-f0116d1dd6fd%2Fhmwo0j8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a) Give an example of a matrix A with rank 3 and nullity 2. Try to give a different example
than your classmates.
(b) If A is any mx n matrix with rank 3 and nullity 2, what can you say about n? Explain.
(c) If A is any matrix mx n with rank 3 and nullity 2, what can you say about m? Explain.
Un ]
2. Suppose 01, 02,..., Un are vectors in Rm and, as usual, write A = [ 0₁ 02
(a) What can you say about the set of vectors V₁, V2,..., Un if rank(A) = m?
(b) What can you say about the set of vectors V1, V2, ..., Un if rank(A) = n?
(c) What can you say about the set of vectors V1, V2,..., Un if nullity (A) = 0?
(d) What can you say about the set of vectors V₁, V2,..., Un if nullity(A) > 0?
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