ম্যাট্রিক্স এর যোগ, বিয়োগ ও গুণ
A=[023−4] A = \left [ \begin{matrix} 0 & 2 \\ 3 & - 4 \end{matrix} \right ] A=[032−4] এবং λ.A=[03a2b24] λ. A = \left [ \begin{matrix} 0 & 3 a \\ 2 b & 24 \end{matrix} \right ] λ.A=[02b3a24] হলে, (λ,a,b)=কত?
(-6,-8,-4)
(-6,4,-9)
(-6,4,9)
(-6,-4,-9)
λ[023−4]=[03a2b24]∴[02λ3λ−4λ]=[03a2b24] \begin{array}{c} \text { } \lambda\left[\begin{array}{cc} 0 & 2 \\ 3 & -4 \end{array}\right]=\left[\begin{array}{cc} 0 & 3 a \\ 2 b & 24 \end{array}\right] \\ \therefore\left[\begin{array}{cc} 0 & 2 \lambda \\ 3 \lambda & -4 \lambda \end{array}\right]=\left[\begin{array}{cc} 0 & 3 a \\ 2 b & 24 \end{array}\right] \end{array} λ[032−4]=[02b3a24]∴[03λ2λ−4λ]=[02b3a24]
ম্যাট্রিক্সের সমতা অনুসারে,
−4λ=242λ=3a3λ=2b∴λ=−6 বा, −12=3a বा, −18=2 b∴a=−4∴b=−9 \begin{array}{l|l|l} -4 \lambda=24 & 2 \lambda=3 a & 3 \lambda=2 b \\ \therefore \lambda=-6 & \text { বा, }-12=3 a & \text { বा, }-18=2 \mathrm{~b} \\ & \therefore \mathrm{a}=-4 & \therefore \mathrm{b}=-9 \end{array} −4λ=24∴λ=−62λ=3a বा, −12=3a∴a=−43λ=2b বा, −18=2 b∴b=−9
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
2A+B= [542−1] \left [ \begin{matrix} 5 & 4 \\ 2 & - 1 \end{matrix} \right ] [524−1] এবং B= [1−117] \left [ \begin{matrix} 1 & - 1 \\ 1 & 7 \end{matrix} \right ] [11−17] হলে A= কত?
A=[−122−5] A = \left [ \begin{matrix} - 1 & 2 \\ 2 & -5 \end{matrix} \right ] A=[−122−5] হলে, A2-2I এর ম্যাট্রিক্সটি কোনটি ?
P=(abca2b2c2a3+1b3+1c3+1) এবং f(x)=x2−3x+5 P=\left(\begin{array}{ccc} a & b & c \\ a^{2} & b^{2} & c^{2} \\ a^{3}+1 & b^{3}+1 & c^{3}+1 \end{array}\right) \text { এবং } f(x)=x^{2}-3 x+5 P=aa2a3+1bb2b3+1cc2c3+1 এবং f(x)=x2−3x+5
