How do you find 2A-3B given A- 5 -2 3 1 - and B- -2 3 1 0 - -

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Standard XII

Mathematics

Multinomial Theorem

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Question

How do you find $2 A - 3 B$ given $A = [\begin{matrix} 5 & - 2 & 3 & 1 \end{matrix}]$ and $B = [\begin{matrix} - 2 & 3 & 1 & 0 \end{matrix}]$ ?

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Solution

Find the value of given expression $2 A - 3 B$ .
Multiplying both sides of the matrix $(A)$ with $2$ :
$\begin{array}{rcl} 2 A & = & 2 \cdot [\begin{matrix} 5 & - 2 & 3 & 1 \end{matrix}] \\ \Rightarrow & 2 A = [\begin{matrix} 10 & - 4 & 6 & 2 \end{matrix}] \end{array}$
Multiplying both sides of the matrix $(B)$ with $3$ :
$\begin{array}{rcl} 3 B & = & 3 . [\begin{matrix} - 2 & 3 & 1 & 0 \end{matrix}] \\ \Rightarrow & 3 B = [\begin{matrix} - 6 & 9 & 3 & 0 \end{matrix}] \end{array}$
The value of $2 A - 3 B$ :
$\begin{array}{rcl} 2 A - 3 B & = & [\begin{matrix} 10 & - 4 & 6 & 2 \end{matrix}] - [\begin{matrix} - 6 & 9 & 3 & 0 \end{matrix}] \\ \Rightarrow & 2 A - 3 B = [\begin{matrix} 16 & - 13 & 3 & 2 \end{matrix}] \end{array}$
Hence, the value of $2 A - 3 B$ is $[\begin{matrix} 16 & - 13 & 3 & 2 \end{matrix}]$ .

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How do you find 2A-3B given A=5-231 and B=-2310 ?

Find the value of given expression 2A-3B.Multiplying both sides of the matrix (A) with 2:2A=2·5-231⇒2A=10-462Multiplying both sides of the matrix (B) with 3:3B=3.-2310⇒3B=-6930The value of 2A-3B:2A-3B=10-462--6930⇒2A-3B=16-1332Hence, the value of 2A-3B is 16-1332.

How do you find $2 A - 3 B$ given $A = [\begin{matrix} 5 & - 2 & 3 & 1 \end{matrix}]$ and $B = [\begin{matrix} - 2 & 3 & 1 & 0 \end{matrix}]$ ?