Question

Find B if B×B=[17 8

8 17].
Matrices​

Answer 1

SOLUTION

TO DETERMINE

The value of B when

$\displaystyle \sf{B \times B = \begin{pmatrix} 17 & 8 \\ 8 & 17 \end{pmatrix} }$

EVALUATION

Let

$\displaystyle \sf{B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} }$

Then

$\displaystyle \sf{B \times B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \times \begin{pmatrix} a & b \\ c & d \end{pmatrix}}$

$\displaystyle \sf{ \implies \: B \times B = \begin{pmatrix} {a}^{2} + bc & ab + bd \\ \\ ac + cd & bc + {d}^{2} \end{pmatrix} }$

Again it is given that

$\displaystyle \sf{B \times B = \begin{pmatrix} 17 & 8 \\ 8 & 17 \end{pmatrix} }$

Comparing we get

$\sf{ {a}^{2} + bc = 17 }$

$\sf{ab + bd = 8 }$

$\sf{ ac + cd = 8 }$

$\sf{ bc + {d}^{2} = 17 }$

Solving we get a = 3 , b = 1 , c = 1 , d = 3

Hence

$\displaystyle \sf{B = \begin{pmatrix} 4 & 1 \\ 1 & 4 \end{pmatrix} }$

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Answer 2

Answer:

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