In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 17. x₁ = x₂ + 2x4 x3 = X4 X2 X3 Determine dim(W) when the components of x satisfy the given conditions. X4 18. X1 + x32x4 = 0 x2 + 2x3 3x4 = 0 -
In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 17. x₁ = x₂ + 2x4 x3 = X4 X2 X3 Determine dim(W) when the components of x satisfy the given conditions. X4 18. X1 + x32x4 = 0 x2 + 2x3 3x4 = 0 -
In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3 x4 = 0 16. x₁ - 2x3 = 0 17. x₁ = x₂ + 2x4 x3 = X4 X2 X3 Determine dim(W) when the components of x satisfy the given conditions. X4 18. X1 + x32x4 = 0 x2 + 2x3 3x4 = 0 -
Linear algebra: please solve q17 correctly and handwritten
Transcribed Image Text:In Exercises 15-20, W is a subspace of R4 consisting of
vectors of the form
X =
15. x₁ - 2x₂ + x3 x4 = 0
16. x₁ - 2x3 = 0
X1
17. x₁ = x₂ + 2x4
x3 =
- X4
X2
X3
Determine dim(W) when the components of x satisfy
the given conditions.
X4
18. XI
+ x3 2x4 = 0
x2 + 2x3 3x4 = 0
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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