W = {y= 2x1 - 3x₂ + x3 -x₁ + 4x2 - 2x3: X1, X2, X3 real}. 2x1 + x2 + 4x3 Exhibit a (3 x 3) matrix A such that W = R(A). Conclude that W is a subspace of R³.
W = {y= 2x1 - 3x₂ + x3 -x₁ + 4x2 - 2x3: X1, X2, X3 real}. 2x1 + x2 + 4x3 Exhibit a (3 x 3) matrix A such that W = R(A). Conclude that W is a subspace of R³.
W = {y= 2x1 - 3x₂ + x3 -x₁ + 4x2 - 2x3: X1, X2, X3 real}. 2x1 + x2 + 4x3 Exhibit a (3 x 3) matrix A such that W = R(A). Conclude that W is a subspace of R³.
Linear algebra: please solve q42 correctly and handwritten
Transcribed Image Text:42. Let
W = {y =
2x13x2 + x3
-x₁ +4x22x3
2x1 + x2 + 4x3
X1, X2, X3 real).
Exhibit a (3 x 3) matrix A such that W = R(A).
Conclude that W is a subspace of R³.
43. Let
X1
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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