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4. Consider the ordered basis E = (₁.e₁-es) for R². If [v] = (1,-1)", then v= e, 4 c H (b) 2e +ez (d) (0,1) C₁ C₁-C₂

4. Consider the ordered basis E = (₁.e₁-es) for R². If [v] = (1,-1)", then v= e, 4 c H (b) 2e +ez (d) (0,1) C₁ C₁-C₂

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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4. Consider the ordered basis E = {e₁.e₁-e₂) for R². If [v] = (1,-1)", then u = A C₁4 C (b) 2e1+0₂ (c) ₁ + ₂ (d) (0.1) e₁
Transcribed Image Text:4. Consider the ordered basis E = {e₁.e₁-e₂) for R². If [v] = (1,-1)", then u = A C₁4 C (b) 2e1+0₂ (c) ₁ + ₂ (d) (0.1) e₁
9. One of the following sets is a subspace of P₁ (a) {f(x) = P₁: f(0) = 1} (b) {f(x) = P₁: f(1) = 1} (c) {f(x) € P₁: f(1) = 0} (d) {f(x) = P₁: f(0) = 0. f(0) = 6} 3 -0. 2 1 10. If A is a 4 x 3 matrix such that N(A) = {0}, and b = (a) It is possible that Az = b has infinitely many solutions (b) The system Ar= b has exactly one solution. (c) The system Ar = b has at most one solution. (d) The system Ar = b has no solution then
Transcribed Image Text:9. One of the following sets is a subspace of P₁ (a) {f(x) = P₁: f(0) = 1} (b) {f(x) = P₁: f(1) = 1} (c) {f(x) € P₁: f(1) = 0} (d) {f(x) = P₁: f(0) = 0. f(0) = 6} 3 -0. 2 1 10. If A is a 4 x 3 matrix such that N(A) = {0}, and b = (a) It is possible that Az = b has infinitely many solutions (b) The system Ar= b has exactly one solution. (c) The system Ar = b has at most one solution. (d) The system Ar = b has no solution then
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