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Levart [38]
3 years ago
8

Find a 2 × 2 matrix b ≠ o and b ≠ i2 such that ab = ba, where a = 1 7 0 1 . b =

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
6 0
If \mathbf A is invertible, then we can simply choose \mathbf B=\mathbf A^{-1} because for any invertible matrix \mathbf X by definition we must have \mathbf{XX}^{-1}=\mathbf X^{-1}\mathbf X=\mathbf I.

We have \det\mathbf A\neq0, as

\det\mathbf A=\begin{vmatrix}1&7\\0&1\end{vmatrix}=1\times1-0\times7=1

which means \mathbf A is non-singular and has an inverse. The inverse itself would be

\mathbf A^{-1}=\dfrac1{\det\mathbf A}\begin{bmatrix}1&0\\-7&1\end{bmatrix}^\top=\begin{bmatrix}1&-7\\0&1\end{bmatrix}
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For the answer to the question above, I'll provide my solutions to my answers for the problem below.

(–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)

(−2x3)(y2)+4x2y3+−3xy4+−1(6x4y)+−1(−5x2y3)+−1(−y5)

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So the answer is,
= <span><span><span><span><span>−<span><span>6x4</span>y</span></span>−<span><span>2x3</span>y2</span></span>+<span><span>9x2</span>y3</span></span>−<span>3xy4</span></span>+y5</span> 

I hope this helps
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<em>Correct </em><em>me </em><em>if</em><em> </em><em>you </em><em>want</em><em> </em><em>If </em><em>its </em><em>wrong</em>

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