Question

Considera las siguientes matrices . Ayuda por favor que es para entregar mañana.

Answer 1

Considerando las matrices A y B se obtiene:

$A+B=\left[\begin{array}{cccc}3&2&4&0\\7&3&5&-3\\-7&3&3&0\end{array}\right]$

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

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

$5A=\left[\begin{array}{cccc}0&10&15&10\\10&5&25&-20\\-20&-5&5&0\end{array}\right]$

$4B=\left[\begin{array}{cccc}12&0&4&-8\\20&8&0&4\\-12&16&8&0\end{array}\right]$

[$(-3)A=\left[\begin{array}{cccc}0&-6&-9&-6\\-6&-3&-15&12\\12&3&-3&0\end{array}\right]$

Explicación paso a paso:

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

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

a. A+B

Suma de matrices;

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

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

$A+B=\left[\begin{array}{cccc}3&2&4&0\\7&3&5&-3\\-7&3&3&0\end{array}\right]$

b. A-B

Resta de matrices;

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

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

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

c. B - A

Resta de matrices;

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

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

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

d. 5A

Multiplicación de un escalar a una matriz;

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

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

$5A=\left[\begin{array}{cccc}0&10&15&10\\10&5&25&-20\\-20&-5&5&0\end{array}\right]$

e. 4B

Multiplicación de un escalar a una matriz;

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

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

$4B=\left[\begin{array}{cccc}12&0&4&-8\\20&8&0&4\\-12&16&8&0\end{array}\right]$

f. (-3)A

Multiplicación de un escalar negativo a una matriz;

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

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

$(-3)A=\left[\begin{array}{cccc}0&-6&-9&-6\\-6&-3&-15&12\\12&3&-3&0\end{array}\right]$

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