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

Solutions > Coin Problems Calculator >

A fair coin is flipped four times. Use a tree diagram to find the probability of observing exactly two heads.

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

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

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

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固有多項式 (

1	2	1
6	−1	0
−1	−2	−1

)

Solution

−λ³−λ²+12λ

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Solution steps

One step at a time

(

1	2	1
6	−1	0
−1	−2	−1

)

行列固有多項式

正方行列 A の固有多項式は det(A−λI) として定義される。ここで, I は A と同じ次数の恒等行列である

(

1	2	1
6	−1	0
−1	−2	−1

)−λ(

1	0	0
0	1	0
0	0	1

)=(

1−λ	2	1
6	−1−λ	0
−1	−2	−1−λ

)

=det(

1−λ	2	1
6	−1−λ	0
−1	−2	−1−λ

)

det(

1−λ	2	1
6	−1−λ	0
−1	−2	−1−λ

)=−λ³−λ²+12λ

=−λ³−λ²+12λ

Coin Problems Examples

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