Question

dadas as matrizes A e B, determine x e y para que A = B*t.
A= [3 1 ]
[4 -2]

B= [x+y x-y]
[1 -2]​

Answer 1

Explicação passo-a-passo:

$A=\left[\begin{array}{ccc}3&1\\4&-2\\\end{array}\right] \\\\\\B=\left[\begin{array}{ccc}x+y&x-y\\1&-2\\\end{array}\right]$

A matriz transposta de B é :

$B^{t} =\left[\begin{array}{ccc}x+y&1\\x-y&-2\\\end{array}\right]$

Calculando x e y;

$A=B^{t} \\\\\left[\begin{array}{ccc}3&1\\4&-2\\\end{array}\right] =\left[\begin{array}{ccc}x+y&1\\x-y&-2\\\end{array}\right]$

Resolvendo o sistema:

$\left \{ {{x+y=3} \atop {x-y=4}} \right.$

Somando as duas equações:

$x+x+y-y=3+4\\\\2x=7\\\\x=\frac{7}{2}$

Substituindo x na primeira equação:

$x+y=3\\\\\frac{7}{2}+y=3\\\\y=3-\frac{7}{2} \\\\y=\frac{6-7}{2}\\\\y=\frac{-1}{2}$