(a) You are told that the rank of matrix A is equal to 3. (i) (ii) What do you understand by this statement? Suggest a matrix whose largest possible rank is equal to matrix A. Explain your answer. (b) The rank of the matrix A is 2. 2 A = |1 k (2 4 3 %3D 1 2. (i) (ii) Determine the value of the constant k. For this value of k, is A invertible? Explain.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.6: More Applications Of Matrix Operations
Problem 11E
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Question 1
(a) You are told that the rank of matrix A is equal to 3.
(i)
(ii)
What do you understand by this statement?
Suggest a matrix whose largest possible rank is equal to matrix A. Explain your
answer.
(b) The rank of the matrix A is 2.
2
1 k 3
(2
4
A =
1 2
(i)
(ii)
Determine the value of the constant k.
For this value of k, is A invertible? Explain.
Transcribed Image Text:Question 1 (a) You are told that the rank of matrix A is equal to 3. (i) (ii) What do you understand by this statement? Suggest a matrix whose largest possible rank is equal to matrix A. Explain your answer. (b) The rank of the matrix A is 2. 2 1 k 3 (2 4 A = 1 2 (i) (ii) Determine the value of the constant k. For this value of k, is A invertible? Explain.
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