Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Let P =
1
- 3
4
U₁ =
3 - 1
0
1
- 5
01
W₂ =
5
■₁ U₂ = ₁ 43
=
3
W3
2
=
V₂
- 8
a. Find a basis (U₁, U2, U3} for R³ such that P is the change-of-coordinates matrix from
{U₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of
represent?]
4
and V3
- 6
3
5
Complete parts (a) and (b).
b. Find a basis {w₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from
{V₁, V₂, V3} to (W₁, W₂, W3}.
W₁ =
P
C← B
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Transcribed Image Text:Let P = 1 - 3 4 U₁ = 3 - 1 0 1 - 5 01 W₂ = 5 ■₁ U₂ = ₁ 43 = 3 W3 2 = V₂ - 8 a. Find a basis (U₁, U2, U3} for R³ such that P is the change-of-coordinates matrix from {U₁, U₂, U3} to the basis {V₁, V2, V3}. [Hint: What do the columns of represent?] 4 and V3 - 6 3 5 Complete parts (a) and (b). b. Find a basis {w₁, W₂, W3} for R³ such that P is the change-of-coordinates matrix from {V₁, V₂, V3} to (W₁, W₂, W3}. W₁ = P C← B
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