limit as x approaches infinity of (3x+9)/(2-x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

implicit derivative tangent volume laplace fourier

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inverse (

0	9	3
2	0	4
3	7	0

)

Solution

(

−1475	750	625
225	−350	125
775	950	−325

)

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Solution steps

One step at a time

(

0	9	3
2	0	4
3	7	0

)⁻¹

Inverse matrix

A matrix is invertible if and only if there is a sequence of elementary row (or column) operations taking it to the identity matrix.

Augment with a 3x3 identity matrix

[

0	9	3	∣	1	0	0
2	0	4	∣	0	1	0
3	7	0	∣	0	0	1

]

Reduce the matrix on the left to the identity matrix

[

1	0	0	∣	−1475	750	625
0	1	0	∣	225	−350	125
0	0	1	∣	775	950	−325

]

The inverse matrix is on the right side of the augmented matrix

−1475	750	625
225	−350	125
775	950	−325

)

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