Question

if a=(3 0/5 1) and b=(-4 2/1 0) find A^2-2ab+b^2​

Answer 1

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}3&0\\5&1\end{array}\right]$

and

$B=\left[\begin{array}{cc}-4&2\\1&0\end{array}\right]$

To Find:A²-2AB+B²

Solution:

We know that

$\bold{A ^{2} -2AB+B^{2} = ( {A -B) }^{2}}$

Step 1: Find A-B

$A-B=\left[\begin{array}{cc}3&0\\5&1\end{array}\right]-\left[\begin{array}{cc}-4&2\\1&0\end{array}\right]$

$A-B=\left[\begin{array}{cc}3+4&0-2\\5-1&1-0\end{array}\right]$

$A-B=\left[\begin{array}{cc}7&-2\\4&1\end{array}\right]$

Step 2: Find (A-B)²

${(A-B)}^2=\left[\begin{array}{cc}7&-2\\4&1\end{array}\right]\times \left[\begin{array}{cc}7&-2\\4&1\end{array}\right]$

${(A-B)}^2=\left[\begin{array}{cc}7(7)+(-2)(4)&7(-2)+(-2)(1)\\4(7)+1(4)&4(-2)+1(1)\end{array}\right]$

${(A-B)}^2=\left[\begin{array}{cc}41&-16\\32&-7\end{array}\right]$

Final answer:

$\bold{\red{A ^{2} -2AB+B^{2} =\left[\begin{array}{cc}41&-16\\32&-7\end{array}\right]}}$

Hope it helps you.

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Answer 2

Answer:

Answer

The correct Answer is

[51 54

−20 −17]