18. Let Q denote the set of all (2 x 2) singular matrices with the usual matrix addition and scalar multipli- cation. Determine whether Q is a vector space.
18. Let Q denote the set of all (2 x 2) singular matrices with the usual matrix addition and scalar multipli- cation. Determine whether Q is a vector space.
18. Let Q denote the set of all (2 x 2) singular matrices with the usual matrix addition and scalar multipli- cation. Determine whether Q is a vector space.
Linear algebra: please solve q18 correctly and handwritten
Transcribed Image Text:erty (c1) of Definition 1. Also show that properties
(c2) and (a3) are not met.
18. Let Q denote the set of all (2 x 2) singular matrices
with the usual matrix addition and scalar multipli-
cation. Determine whether Q is a vector space.
1
22 Prove property 3 of Theorem 1
of
Hint: Note that
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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