Question

60) Let H = \begin{Bmatrix} \begin{bmatrix} a & b \\ b & c \end{bmatrix} : a, b, c \in \mathbb{R} \end{Bmatrix} Find the dimension of the subspace H. A) dim H = 1 B) dim H = 3 C) dim H = 4 D) dim H = 2

          60) Let H = \begin{Bmatrix} \begin{bmatrix} a & b \\ b & c \end{bmatrix} : a, b, c \in \mathbb{R} \end{Bmatrix}
Find the dimension of the subspace H.
A) dim H = 1
B) dim H = 3
C) dim H = 4
D) dim H = 2

60) Let H =
< b m a t r i x >
: a, b, c ∈ℝ
Find the dimension of the subspace H.
A) dim H = 1
B) dim H = 3
C) dim H = 4
D) dim H = 2

Added by Hugo J.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Srilakshmi E K

09/16/2021

Step 1

Step 1: The subspace H is spanned by the matrices $$\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}$$, $$\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$, $$\begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix}$$. Show more…

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60) Let H = { $$\begin{bmatrix} a & b \\ b & c \end{bmatrix}$$ : a, b, c in R } Find the dimension of the subspace H. A) dim H = 1 B) dim H = 3 C) dim H = 4 D) dim H = 2