3. Determine whether the set is a subspace of the vector space M2. Explain your answers. а 0 (a) The set of all matrices of the form 1 b а 0 (b) The set of all matrices of the form where a + b = 0.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Linear Algebra

**Problem 3: Determine whether the set is a subspace of the vector space \( M_{22} \). Explain your answers.**

**(a)** The set of all matrices of the form:

\[
\begin{bmatrix}
a & 0 \\
1 & b
\end{bmatrix}
\]

**(b)** The set of all matrices of the form:

\[
\begin{bmatrix}
a & 0 \\
0 & b
\end{bmatrix}
\]

where \( a + b = 0 \).
Transcribed Image Text:**Problem 3: Determine whether the set is a subspace of the vector space \( M_{22} \). Explain your answers.** **(a)** The set of all matrices of the form: \[ \begin{bmatrix} a & 0 \\ 1 & b \end{bmatrix} \] **(b)** The set of all matrices of the form: \[ \begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix} \] where \( a + b = 0 \).
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