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Jawaban:

Matriks

Penjelasan dengan langkah-langkah:

4x -5y=9

-x+3y=-11

(4 -5) (x) = ( 9)

(-1 3) (y) (-11)

AX=B

X=A⁻¹.B

X=(x) A=(4 –5) B=( 9)

(y) (–1 3) (–11)

Invers

A = ( 4 –5)

(–1 3)

(4 –5) = 1 (3 5)

(–1 3) (4×3)-(-5x-1) (1 4)

= 1 (3 5)

(12) – (5) (1 4)

= 1 (3 5)

7 (1 4)

= (3/7 5/7)

(1/7 4/7)

(x)=(3/7 5/7) ( 9)

(y) (1/7 4/7) (-11)

(x)=(3/7×9 + 5/7x-11)

(y) (1/7×9 + 4/7x-11)

(x)=(27/7 + -55/7)

(y)=(9/7 + -44/7)

(x)=(-28/7)

(y)=(-35/7)

(x)=(-4)

(y)=(-5)

Pembuktian

(4 -5) (-4) = (9)

(-1 3) (-5) (-11)

(4x-4 + -5x-5) = (9)

(-1x-4 + 3x-5) (-11)

(-16 + 25) = (9)

(4 + -15) (-11)

(9) = (9) => sama => benar

(-11)=(-11)

Demikian

Semoga membantu dan bermanfaat!