Question

alguém me ajuda com essa matrize​

Answer 1

Resposta:

.

Explicação passo-a-passo:

a)

$A = \left[\begin{array}{ccc}0&2\\4&-2\\\end{array}\right] \\\\DetA = 0.(-2) - 2.4\\DetA = -8\\\\A^{-1} = DetA^{-1}.\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]\\A^{-1} = 1/DetA. \left[\begin{array}{ccc}-2&-2\\-4&0\\\end{array}\right]\\A^{-1} = -1/8. \left[\begin{array}{ccc}-2&-2\\-4&0\\\end{array}\right]\\A^{-1} = \left[\begin{array}{ccc}1/4&1/4\\1/2&0\\\end{array}\right]$

$B = \left[\begin{array}{ccc}-6&2\\6&-3\\\end{array}\right]\\\\DetB = (-6).(-3) - 6.2\\DetB = 6\\\\B^{-1} = DetB^{-1}.\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]\\B^{-1} = 1/6.\left[\begin{array}{ccc}-3&-2\\-6&-6\\\end{array}\right]\\B^{-1} =\left[\begin{array}{ccc}-1/2&-1/3\\-1&-1\\\end{array}\right]$

b)

$A^{-1}.B^{-1}\\\\\left[\begin{array}{ccc}1/4&1/4\\1/2&0\\\end{array}\right].\left[\begin{array}{ccc}-1/2&-1/3\\-1&-1\\\end{array}\right]\\\\A_{1,1} = 1/4.(-1/2) + 1/4.(-1) = -1/8 -1/4 = -12/32 = -3/8\\A_{1,2} = 1/4.(-1/3) + 1/4.(-1) = -1/12 - 1/4 = -16/48 = -1/3\\A_{2,1} = 1/2.(-1/2) + 0.(-1) = -1/4\\A_{2,2} = 1/2.(-1/3) + 0.(-1)=-1/6\\\\\left[\begin{array}{ccc}-3/8&-1/3\\-1/4&-1/6\\\end{array}\right]$

c)

$B^{-1}.A^{-1}\\\\\left[\begin{array}{ccc}-1/2&-1/3\\-1&-1\\\end{array}\right].\left[\begin{array}{ccc}1/4&1/4\\1/2&0\\\end{array}\right]\\\\A_{1,1} = (-1/2).1/4 + (-1/3).1/2 = -1/8-1/6 = -14/48 = -7/24\\A_{1,2} = (-1/2).1/4 + (-1/3).0 = -1/8\\A_{2,1} = (-1).1/4+(-1).1/2 = -1/4-1/2 = -6/8 = -3/4\\A_{2,2} = (-1).1/4+(-1).0 = -1/4\\\\\left[\begin{array}{ccc}-7/24&-1/8\\-3/4&-1/4\\\end{array}\right]$

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