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Let A be the 100 by 100 matrix whose i, j entry is (−1)²-¹ + 2/-¹. For example, the top left 3 x 3 corner of A is +1 1+ 4 -1+4 1+4 A = +1 1+1 1+2 -1+2 1+2 8 ... www Let b be the 100 by 1 column vector (1,0, –1,0, ... 0)7, whose first and third entry are nonzero but whose last 97 entries are all 0. (Note that the superscript T denotes transpose.) a. Compute the vector Ab (i.e. matrix A times vector 5) b. Compute the vector ¹ A.

Let A be the 100 by 100 matrix whose i, j entry is (−1)²-¹ + 2/-¹. For example, the top left 3 x 3 corner of A is +1 1+ 4 -1+4 1+4 A = +1 1+1 1+2 -1+2 1+2 8 ... www Let b be the 100 by 1 column vector (1,0, –1,0, ... 0)7, whose first and third entry are nonzero but whose last 97 entries are all 0. (Note that the superscript T denotes transpose.) a. Compute the vector Ab (i.e. matrix A times vector 5) b. Compute the vector ¹ A.

Advanced Engineering Mathematics
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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Let A be the 100 by 100 matrix whose i, j entry is (-1)²-¹ + 2/-¹. For example, the top left 3 x 3 corner of A is +1 A = -1+1 1+1 1+2 -1+2 1+2 8 1+4 -1+4 1+4 ... *** Let b be the 100 by 1 column vector (1,0, –1,0, ... 0)7, whose first and third entry are nonzero but whose last 97 entries are all 0. (Note that the superscript 7 denotes transpose.) a. Compute the vector Ab (i.e. matrix A times vector b) b. Compute the vector ¹ A.
Transcribed Image Text:Let A be the 100 by 100 matrix whose i, j entry is (-1)²-¹ + 2/-¹. For example, the top left 3 x 3 corner of A is +1 A = -1+1 1+1 1+2 -1+2 1+2 8 1+4 -1+4 1+4 ... *** Let b be the 100 by 1 column vector (1,0, –1,0, ... 0)7, whose first and third entry are nonzero but whose last 97 entries are all 0. (Note that the superscript 7 denotes transpose.) a. Compute the vector Ab (i.e. matrix A times vector b) b. Compute the vector ¹ A.
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