If the matrices [MATH]D_{1}[/MATH] and [MATH]Y_{1}[/MATH] are solutions the a system of linear equations of type [MATH]AX = B[/MATH], and [MATH]aD_{1} + bY_{1}[/MATH] is also a solution then [MATH]B = 0[/MATH] (null matrix)?
From what I see: [MATH]D_{1} = A^{-1}B[/MATH] and [MATH]Y_{1} = A^{-1}B[/MATH] also.
Then [MATH]a(AA^{-1}B) + b(AA^{-1}B) = B \Leftrightarrow aB + bB = B[/MATH]. [MATH]B = 0[/MATH] is true only if [MATH]a,b \neq \frac{1}{2}[/MATH].
But the book has it for any [MATH]a,b \in {R}[/MATH].
Sorry for the real numbers LaTeX representation, I don't know any better.
From what I see: [MATH]D_{1} = A^{-1}B[/MATH] and [MATH]Y_{1} = A^{-1}B[/MATH] also.
Then [MATH]a(AA^{-1}B) + b(AA^{-1}B) = B \Leftrightarrow aB + bB = B[/MATH]. [MATH]B = 0[/MATH] is true only if [MATH]a,b \neq \frac{1}{2}[/MATH].
But the book has it for any [MATH]a,b \in {R}[/MATH].
Sorry for the real numbers LaTeX representation, I don't know any better.