Mathematics for Data Science II, Week-wise practice

Undated, Set week-03

Learning mode

Question 1

+3−0Multiple correct

Which of the following sets are subspaces of the corresponding vector space (of $\mathbb R^3$ , $\mathbb R^2$ , polynomials or matrices as indicated)? Select all.

Select all that apply.

A.
$\{(x,y): x^2=y^2\}$
B.
the set of all polynomials of degree at most 3
C.
$\{(x,y): xy=0\}$
D.
the set of all invertible $2\times2$ matrices
E.
$\{(x,y,z): x+2y-z=0\}$
F.
the set of polynomials $p(x)$ with $p(1)=0$

Mathematics for Data Science II, Week-wise practice

Undated, Set week-03

Learning mode

Question 1

+3−0Multiple correct

Which of the following sets are subspaces of the corresponding vector space (of $\mathbb R^3$ , $\mathbb R^2$ , polynomials or matrices as indicated)? Select all.

Select all that apply.

A.
$\{(x,y): x^2=y^2\}$
B.
the set of all polynomials of degree at most 3
C.
$\{(x,y): xy=0\}$
D.
the set of all invertible $2\times2$ matrices
E.
$\{(x,y,z): x+2y-z=0\}$
F.
the set of polynomials $p(x)$ with $p(1)=0$

Question 1

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Question 1

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