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52. Let H = 5 Span {V₁, V₂} and K = Span {V3, V4}, where 2 -------- V3 4 = 3 = V4 0 -12 -28 8 5 Then H and K are subspac
Posted: Tue Jul 12, 2022 12:40 pm
by answerhappygod
- 52 Let H 5 Span V V And K Span V3 V4 Where 2 V3 4 3 V4 0 12 28 8 5 Then H And K Are Subspac 1 (72.54 KiB) Viewed 29 times
52. Let H = 5 Span {V₁, V₂} and K = Span {V3, V4}, where 2 -------- V3 4 = 3 = V4 0 -12 -28 8 5 Then H and K are subspaces of R³. In fact, H and K are planes in R3³ through the origin, and they intersect in a line through 0. Find a nonzero vector w that gen- erates that line. [Hint: w can be written as C₁V₁ + C2V2 and also as c3V3 + C4V4. To build w, solve the equation C₁V₁ + C₂V₂ = C3V3 + C4V4 for the unknown c;'s.]