Question

9 The dimension of a linear space does not depend on a choice of ....
(A)Basis
(B) Solution
(C)Differential equation
(D)None of these​

Answer 1

Answer:

The dimension of a linear does not depend on a choice of none of these.

Step-by-step explanation:

Dimension of linear space:

• The dimension of a linear space is defined as the cardinality of its bases.
• The number of vectors in a basis for V is called a dimension of V.
• Dimension is denoted by dim(v).

Example:

• The dimension of Rⁿ is n.
• The dimension of the vector space of polynomials in x with real coefficients having degree atmost 2 is 3.
• A vector space that consists of only zero vector has dimension zero.

Basis:

• Let V be a vector space. A minimal set of vectors in V that spans V is called a basis of V.
• The Basis for V is a set of vectors that is linearly independent and it spans V.
• So, the dimension of a linear space depends on basis and also the solution.
• Also the dimension linear space depends on differential equation.

Know more about  Dimensions:

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