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Q1: 1 2 3 1. Matrix A =| 2 3 4 is symmetric. 3 3 4 2 1 2. If { 1 1 } is a basis in R 2 3. { 0 is an orthogonal basis in R3 2 spans R2. 4 1) 1 5. {- is an orthonormal basis in R³ 0) V2 0 0 2 6. det 0 3 2 =7 1 4 4.

Q1: 1 2 3 1. Matrix A =| 2 3 4 is symmetric. 3 3 4 2 1 2. If { 1 1 } is a basis in R 2 3. { 0 is an orthogonal basis in R3 2 spans R2. 4 1) 1 5. {- is an orthonormal basis in R³ 0) V2 0 0 2 6. det 0 3 2 =7 1 4 4.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Q1: (1 2 3 1. Matrix A =| 2 3 4 is symmetric. 3 3 4 2 2 1 2. If { 1 1 1 } is a basis in R³ 2 2 2 2 3. { 0 1 is an orthogonal basis in R³ 1 4. 2 2 spans R². 1 5. {- V2(0)2 1 is an orthonormal basis in R³ 0 0 2 6. det 0 3 2 =7 1 4 Q2: 1. The Nullspace is defined only for square matrices. 2. C, and N, have the same dimension called rankA. 3. dim C,+dim R, = ncolumns of A 4. C = R, 5. If Basis(H) =0 then Basis(H-)= 1 6. If det A = 0 then dim N, = 0 ▪ Q3: 1. If (v,,v,) = 0 then || v ||° +|| v ||°=|| v, + v,|| 2. (v,,v;) =|| v || 3. If V = v, x v, then (V,v,)= (V,v,)=1. 4. || av ||= a || v | V2 5. If (v,,v,) = 0 then v, || v, 6. if v, || V2 then v,×v, = 0
Transcribed Image Text:Q1: (1 2 3 1. Matrix A =| 2 3 4 is symmetric. 3 3 4 2 2 1 2. If { 1 1 1 } is a basis in R³ 2 2 2 2 3. { 0 1 is an orthogonal basis in R³ 1 4. 2 2 spans R². 1 5. {- V2(0)2 1 is an orthonormal basis in R³ 0 0 2 6. det 0 3 2 =7 1 4 Q2: 1. The Nullspace is defined only for square matrices. 2. C, and N, have the same dimension called rankA. 3. dim C,+dim R, = ncolumns of A 4. C = R, 5. If Basis(H) =0 then Basis(H-)= 1 6. If det A = 0 then dim N, = 0 ▪ Q3: 1. If (v,,v,) = 0 then || v ||° +|| v ||°=|| v, + v,|| 2. (v,,v;) =|| v || 3. If V = v, x v, then (V,v,)= (V,v,)=1. 4. || av ||= a || v | V2 5. If (v,,v,) = 0 then v, || v, 6. if v, || V2 then v,×v, = 0
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