Basis and Dimension

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Which is your favorite mathematical subject?

• Linear Algebra

• Real Analysis

• Partial Differential Equations

• Sequence and Series

A set of linear equations is represented by the matrix equation Ax=b. The necessary condition for the existence of a solution for this system is

• A must be invertible

• b must be linearly dependent on columns of A

• b must be linearly independent of columns of A

• None of these

Which of the following would be a linear combination of {(a, 0), (b, 0)} ? (a and b are non-zero)

• (3,0)

• (1, 3)

• (0,5)

• (16, 0)

Define Dimension of a vector space?

Basis of a vector space are unique.

• True

• False

 Which of the following are linearly independent of  $R^2$  ?

• {(1,0), (0,1)}

• {(1,1), (1,2)}

• {(2,3), (4,6)}

• {(2,0)}

• {(1,0),(3,0)}
  

Which of the following is a basis for $R^2$ ?

• {(1,0), (0,1)}

• {(2,0)}

• {(1,2), (2,3), (1,7)}

• {(1,3),(2, 4) }

• {(1,0), (2,0)}

What is the dimension of $C^2\left(R\right)$  ?

• 2

• 3

• 4

• 1

What is the dimension of real polynomial of degree n over the set of reals?

• n

• n-1

• n+1

• not defined