If `A= [[3],[5],[2]]` and B=[1 0 4] , Verify that `(Ab)^T=B^Ta^T` - Mathematics

प्रश्न

If $A = [\begin{matrix} 3 \\ 5 \\ 2 \end{matrix}]$ And B=[1 0 4] , Verify that ${(A B)}^{T} = B^{T} A^{T}$

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उत्तर

$G i v e n : A = [\begin{matrix} 3 \\ 5 \\ 2 \end{matrix}]$

$A^{T} = [\begin{matrix} 3 & 5 & 2 \end{matrix}]$

$B = [\begin{matrix} 1 & 0 & 4 \end{matrix}]$

$B^{T} = [\begin{matrix} 1 \\ 0 \\ 4 \end{matrix}]$

$N o w,$

$A B = [\begin{matrix} 3 \\ 5 \\ 2 \end{matrix}] [\begin{matrix} 1 & 0 & 4 \end{matrix}]$

$\Rightarrow A B = [\begin{matrix} 3 & 0 & 12 \\ 5 & 0 & 20 \\ 2 & 0 & 8 \end{matrix}]$

$\Rightarrow {(A B)}^{T} = [\begin{matrix} 3 & 5 & 2 \\ 0 & 0 & 0 \\ 12 & 20 & 8 \end{matrix}] . . . (1)$

$B^{T} A^{T} = [\begin{matrix} 1 \\ 0 \\ 4 \end{matrix}] [\begin{matrix} 3 & 5 & 2 \end{matrix}]$

$\Rightarrow B^{T} A^{T} = [\begin{matrix} 3 & 5 & 2 \\ 0 & 0 & 0 \\ 12 & 20 & 8 \end{matrix}] . . . (2)$

$\Rightarrow {(A B)}^{T} = B^{T} A^{T} [From eqs . (1) and (2)]$

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Algebraic Operations on Matrices - Multiplication of Matrices

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Q 2 Q 1.4 Q 3.1

पाठ 5: Algebra of Matrices - Exercise 5.4 [पृष्ठ ५४]

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पाठ 5 Algebra of Matrices
Exercise 5.4 | Q 2 | पृष्ठ ५४

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If $A = [\begin{matrix} 3 \\ 5 \\ 2 \end{matrix}]$ and B=[1 0 4] , Verify that ${(A b)}^{T} = B^{T} a^{T}$ - Mathematics

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If A=[352] and B=[1 0 4] , Verify that (Ab)T=BTaT - Mathematics

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If $A = [\begin{matrix} 3 \\ 5 \\ 2 \end{matrix}]$ and B=[1 0 4] , Verify that ${(A b)}^{T} = B^{T} a^{T}$ - Mathematics

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