ম্যাট্রিক্স এর যোগ, বিয়োগ ও গুণ
A=[4235] A=\left[\begin{array}{ll}4 & 2 \\ 3 & 5\end{array}\right] A=[4325] হলে A2−5A+6I′ A^{2}-5 A+6 I^{\prime} A2−5A+6I′ নির্ণয় কর, যেখানে, I=[1001] \mathrm{I}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] I=[1001]
[−8−81212]\left[\begin{array}{cc} -8 & -8 \\ 12 & 12 \end{array}\right][−812−812]
[981212]\left[\begin{array}{cc} 9 & 8 \\ 12 & 12 \end{array}\right][912812]
[881212]\left[\begin{array}{cc} 8 & 8 \\ 12 & 12 \end{array}\right][812812]
[−88−1212]\left[\begin{array}{cc} -8 & 8 \\ -12 & 12 \end{array}\right][−8−12812]
Solve: A2−5 A+6I \mathrm{A}^{2}-5 \mathrm{~A}+6 \mathrm{I} A2−5 A+6I
=[4235][4235]−5[4235]+6[1001]=[16+68+1012+156+25]−[20101525]+[6006]=[22182731]−[20101525]+[6006]=[22−20+618−10+027−15+031−25+6]=[881212] (Ans.) \begin{array}{l} =\left[\begin{array}{ll} 4 & 2 \\ 3 & 5 \end{array}\right]\left[\begin{array}{ll} 4 & 2 \\ 3 & 5 \end{array}\right]-5\left[\begin{array}{ll} 4 & 2 \\ 3 & 5 \end{array}\right]+6\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \\ =\left[\begin{array}{ll} 16+6 & 8+10 \\ 12+15 & 6+25 \end{array}\right]-\left[\begin{array}{ll} 20 & 10 \\ 15 & 25 \end{array}\right]+\left[\begin{array}{ll} 6 & 0 \\ 0 & 6 \end{array}\right] \\ =\left[\begin{array}{ll} 22 & 18 \\ 27 & 31 \end{array}\right]-\left[\begin{array}{ll} 20 & 10 \\ 15 & 25 \end{array}\right]+\left[\begin{array}{ll} 6 & 0 \\ 0 & 6 \end{array}\right] \\ =\left[\begin{array}{ll} 22-20+6 & 18-10+0 \\ 27-15+0 & 31-25+6 \end{array}\right] \\ =\left[\begin{array}{cc} 8 & 8 \\ 12 & 12 \end{array}\right] \text { (Ans.) } \\ \end{array} =[4325][4325]−5[4325]+6[1001]=[16+612+158+106+25]−[20151025]+[6006]=[22271831]−[20151025]+[6006]=[22−20+627−15+018−10+031−25+6]=[812812] (Ans.)
A=[21−1] A=\left[\begin{array}{lll}2 & 1 & -1\end{array}\right] A=[21−1] এবং B=[203] B=\left[\begin{array}{l}2 \\ 0 \\ 3\end{array}\right] B=203 হলে, BA= \mathrm{BA}= BA= ?
A=[22−1303232],B=[x1x2x3] \mathrm{A}=\left[\begin{array}{ccc}2 & 2 & -1 \\ 3 & 0 & 3 \\ 2 & 3 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{l}\mathrm{x}_{1} \\ \mathrm{x}_{2} \\ \mathrm{x}_{3}\end{array}\right] A=232203−132,B=x1x2x3 এবং C=[5711] \mathrm{C}=\left[\begin{array}{c}5 \\ 7 \\ 11\end{array}\right] C=5711
A=[1234],B=[1001] A = \left [ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right ] , B = \left [ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right ] A=[1324],B=[1001]
AT – BT = কত?
A=[1,2,3],BA=[246369123] \mathbf{A}=[\mathbf{1 , 2 , 3}], B A=\left[\begin{array}{lll}2 & 4 & 6 \\ 3 & 6 & 9 \\ 1 & 2 & 3\end{array}\right] A=[1,2,3],BA=231462693 হলে B ম্যাট্রিক্সটি নির্ণয় করো।
