Matrix Inverse Calculator - Free Online Calculator With Steps & Examples

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

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Steps Examples

Generated by AI

(

1	3	5	9
1	3	1	7
4	3	9	7
5	2	0	9

)⁻¹

Solution

(

−1347	247	747	647
−58	78	14	−14
39376	−53376	13188	−9188
55188	−41188	−1394	994

)

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Solution steps

One step at a time

(

1	3	5	9
1	3	1	7
4	3	9	7
5	2	0	9

)⁻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 4x4 identity matrix

[

1	3	5	9	∣	1	0	0	0
1	3	1	7	∣	0	1	0	0
4	3	9	7	∣	0	0	1	0
5	2	0	9	∣	0	0	0	1

]

Reduce the matrix on the left to the identity matrix

[

1	0	0	0	∣	−1347	247	747	647
0	1	0	0	∣	−58	78	14	−14
0	0	1	0	∣	39376	−53376	13188	−9188
0	0	0	1	∣	55188	−41188	−1394	994

]

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

−1347	247	747	647
−58	78	14	−14
39376	−53376	13188	−9188
55188	−41188	−1394	994

)

Matrix Inverse Examples

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

Matrix Inverse Calculator - Free Online Calculator With Steps & Examples

Solution

Solution steps

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