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Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i) and (1,1,1,1) in C^4 over C. The dimension of W over C is?
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Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i)...


Dimension of the subspace W


  1. Definition of subspace: A subspace W of a vector space V is a subset of V that is closed under addition and scalar multiplication.


  2. Span of vectors: The subspace W spanned by the given vectors is the set of all possible linear combinations of the given vectors.


  3. Linear independence: To find the dimension of W, we need to determine the number of linearly independent vectors in the set.


  4. Row reduction: We can create a matrix with the given vectors as rows and perform row reduction to determine the number of linearly independent vectors.


  5. Dimension of W: The dimension of W is equal to the number of linearly independent vectors in the set.


  6. Calculations: By performing row reduction, we find that the set of vectors is linearly independent, and therefore the dimension of W is 4.

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Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i)...
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Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i) and (1,1,1,1) in C^4 over C. The dimension of W over C is?
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Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i) and (1,1,1,1) in C^4 over C. The dimension of W over C is? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i) and (1,1,1,1) in C^4 over C. The dimension of W over C is? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let W be the subspace spanned by (2i,0,1,2i),(0,2i-2,i-3,0),(-i,1,0,i) and (1,1,1,1) in C^4 over C. The dimension of W over C is?.
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