Choosen-one, let's knock this out.
Here are the solutions to your matrix problems:
1) Find 2A+B
Given A=(1021) and B=(3210).
Step 1: Calculate 2A.
2A=2(1021)=(2×12×02×22×1)=(2042)
Step 2: Add 2A and B.
2A+B=(2042)+(3210)=(2+30+24+12+0)=(5252)
The result is:
\begin{pmatrix 5 & 5 \\ 2 & 2 \end{pmatrix}}
2) Express D2 as a single matrix
Given D=(5−7−21).
Step 1: Calculate D2=D×D.
D2=(5−7−21)(5−7−21)
D2=((5)(5)+(−2)(−7)(−7)(5)+(1)(−7)(5)(−2)+(−2)(1)(−7)(−2)+(1)(1))
D2=(25+14−35−7−10−214+1)
D2=(39−42−1215)
The result is:
\begin{pmatrix 39 & -12 \\ -42 & 15 \end{pmatrix}}
3) Find GH
Given G=(32−2−1) and H=(71).
Step 1: Multiply matrix G by matrix H.
GH=(32−2−1)(71)
GH=((3)(7)+(−2)(1)(2)(7)+(−1)(1))
GH=(21−214−1)
GH=(1913)
The result is:
\begin{pmatrix 19 \\ 13 \end{pmatrix}}
4) Find MN
Given M=(8−5−43) and N=(13).
Step 1: Multiply matrix M by matrix N.
MN=(8−5−43)(13)
MN=((8)(1)+(−4)(3)(−5)(1)+(3)(3))
MN=(8−12−5+9)
MN=(−44)
The result is:
\begin{pmatrix -4 \\ 4 \end{pmatrix}}
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