Find if possible the matrices: a) AB b) BA. A=[3−215],B=[005−6]

Step 1 It is given that, A=[3−215],B=[005−6] We have to find if possible the matrices: a) AB b) BA. Step 2 We have , A=[3−215],B=[005−6] a) AB ⇒AB=[3−215]⋅[005−6] ⇒AB=[3×0+(−2)53×0+(−2)(−6)1×0+5×51×0+5(−6)] ⇒AB=[−101225−30] Hence , AB=[−101225−30] b) BA ⇒BA=[005−6]⋅[3−215] ⇒BA=[0×3+0×10×(−2)+0×55×3+(−6)×15×(−2)+(−6)×5] ⇒BA=[009−40] Hence , BA=[009−40]

Answered: "Find if possible the matrices: a) AB b)..."

opatovaL

Answered question

2021-02-25

Find if possible the matrices: a) AB b) BA.

A = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}], B = [\begin{matrix} 0 & 0 \\ 5 & - 6 \end{matrix}]

Answer & Explanation

Arnold Odonnell

Skilled2021-02-26Added 109 answers

Step 1
It is given that,

A = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}], B = [\begin{matrix} 0 & 0 \\ 5 & - 6 \end{matrix}]

We have to find if possible the matrices:
a) AB b) BA.
Step 2
We have ,

A = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}], B = [\begin{matrix} 0 & 0 \\ 5 & - 6 \end{matrix}]

a) AB

\Rightarrow A B = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}] \cdot [\begin{matrix} 0 & 0 \\ 5 & - 6 \end{matrix}]

\Rightarrow A B = [\begin{matrix} 3 \times 0 + (- 2) 5 & 3 \times 0 + (- 2) (- 6) \\ 1 \times 0 + 5 \times 5 & 1 \times 0 + 5 (- 6) \end{matrix}]

\Rightarrow A B = [\begin{matrix} - 10 & 12 \\ 25 & - 30 \end{matrix}]

Hence ,

A B = [\begin{matrix} - 10 & 12 \\ 25 & - 30 \end{matrix}]

b) BA

\Rightarrow B A = [\begin{matrix} 0 & 0 \\ 5 & - 6 \end{matrix}] \cdot [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}]

\Rightarrow B A = [\begin{matrix} 0 \times 3 + 0 \times 1 & 0 \times (- 2) + 0 \times 5 \\ 5 \times 3 + (- 6) \times 1 & 5 \times (- 2) + (- 6) \times 5 \end{matrix}]

\Rightarrow B A = [\begin{matrix} 0 & 0 \\ 9 & - 40 \end{matrix}]

Hence ,

B A = [\begin{matrix} 0 & 0 \\ 9 & - 40 \end{matrix}]

Jeffrey Jordon

Expert2022-01-14Added 2575 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2022-08-23Added 2575 answers

Answer is given below (on video)

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