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In Exercises 1-2, find the rank and nullity of the matrix A by reducing it to row echelon form. 1. 17 2 1. (a) A = 3 3 4 -2 (b) A = 6 -1 2 -4 5 -4 3. 00 2. 246 00

In Exercises 1-2, find the rank and nullity of the matrix A by reducing it to row echelon form. 1. 17 2 1. (a) A = 3 3 4 -2 (b) A = 6 -1 2 -4 5 -4 3. 00 2. 246 00

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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Q4) > In Exercises 1–2, find the rank and nullity of the matrix A by reducing it to row echelon form. 2 -1 4 -2 1. (a) A = -3 3 4 8 -4 4 -2 3 (b) A =| -3 -1 -4 5 8 -2 1 -1 -3 1 3 2. (a) A = -2 -1 -1 3 3 37 (b) A = | -3 -1 4 -2 1 -4 -2 Q5) > In Exercises 33–34, let u = (u1, U2, U3) and v= (V1, V2, Vz). Show that the expression does not define an inner product on R, and list all inner product axioms that fail to hold. 33. (u, v) = u¡v} + užuš + užu} 34. (u, v) = u į Vj – U2V2 + uUz Vz > In Exercises 35-36, suppose that u and v are vectors in an in- ner product space. Rewrite the given expression in terms of (u, v), |u', and ||v||². 35. (2v – 4u, u – 3v) 36. (Su + 6r, 4v -Зu)
Transcribed Image Text:Q4) > In Exercises 1–2, find the rank and nullity of the matrix A by reducing it to row echelon form. 2 -1 4 -2 1. (a) A = -3 3 4 8 -4 4 -2 3 (b) A =| -3 -1 -4 5 8 -2 1 -1 -3 1 3 2. (a) A = -2 -1 -1 3 3 37 (b) A = | -3 -1 4 -2 1 -4 -2 Q5) > In Exercises 33–34, let u = (u1, U2, U3) and v= (V1, V2, Vz). Show that the expression does not define an inner product on R, and list all inner product axioms that fail to hold. 33. (u, v) = u¡v} + užuš + užu} 34. (u, v) = u į Vj – U2V2 + uUz Vz > In Exercises 35-36, suppose that u and v are vectors in an in- ner product space. Rewrite the given expression in terms of (u, v), |u', and ||v||². 35. (2v – 4u, u – 3v) 36. (Su + 6r, 4v -Зu)
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