Show that $8$ is an eigen value of $A$
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Consider the following matrix:
$$A=beginbmatrixB&&&C\D&&&Fendbmatrix$$ where
$$B= beginbmatrix 9 &1&1&1&1\1&9&1&1&1\1&1&9&1&1\1&1&1&9&1\1&1&1&1&9endbmatrix$$ and $$C=beginbmatrix1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1endbmatrix$$
and $$D=C^T$$
and $$F=beginbmatrix G&H \I &Jendbmatrix$$
where $$G=beginbmatrix 8 &1&1&1\1&8&1&1\1&1&8&1\1&1&1&8endbmatrix$$ and $$H=beginbmatrix 0\0\0\0endbmatrix$$ and $$I=H^T$$ and
$$J=beginbmatrix 5endbmatrix$$
Show that $8$ is an eigen value of the matrix $A$.
How should I try to prove it?Please give some hints .I dont want a complete solution
linear-algebra matrices eigenvalues-eigenvectors
asked Aug 23 at 3:39
PureMathematics
976
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up vote
4
down vote
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Consider the following matrix:
$$A=beginbmatrixB&&&C\D&&&Fendbmatrix$$ where
$$B= beginbmatrix 9 &1&1&1&1\1&9&1&1&1\1&1&9&1&1\1&1&1&9&1\1&1&1&1&9endbmatrix$$ and $$C=beginbmatrix1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1endbmatrix$$
and $$D=C^T$$
and $$F=beginbmatrix G&H \I &Jendbmatrix$$
where $$G=beginbmatrix 8 &1&1&1\1&8&1&1\1&1&8&1\1&1&1&8endbmatrix$$ and $$H=beginbmatrix 0\0\0\0endbmatrix$$ and $$I=H^T$$ and
$$J=beginbmatrix 5endbmatrix$$
Show that $8$ is an eigen value of the matrix $A$.
How should I try to prove it?Please give some hints .I dont want a complete solution
linear-algebra matrices eigenvalues-eigenvectors
asked Aug 23 at 3:39
PureMathematics
976
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
Consider the following matrix:
$$A=beginbmatrixB&&&C\D&&&Fendbmatrix$$ where
$$B= beginbmatrix 9 &1&1&1&1\1&9&1&1&1\1&1&9&1&1\1&1&1&9&1\1&1&1&1&9endbmatrix$$ and $$C=beginbmatrix1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1endbmatrix$$
and $$D=C^T$$
and $$F=beginbmatrix G&H \I &Jendbmatrix$$
where $$G=beginbmatrix 8 &1&1&1\1&8&1&1\1&1&8&1\1&1&1&8endbmatrix$$ and $$H=beginbmatrix 0\0\0\0endbmatrix$$ and $$I=H^T$$ and
$$J=beginbmatrix 5endbmatrix$$
Show that $8$ is an eigen value of the matrix $A$.
How should I try to prove it?Please give some hints .I dont want a complete solution
linear-algebra matrices eigenvalues-eigenvectors
asked Aug 23 at 3:39
PureMathematics
976
Consider the following matrix:
$$A=beginbmatrixB&&&C\D&&&Fendbmatrix$$ where
$$B= beginbmatrix 9 &1&1&1&1\1&9&1&1&1\1&1&9&1&1\1&1&1&9&1\1&1&1&1&9endbmatrix$$ and $$C=beginbmatrix1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1\1&1&1&1&1endbmatrix$$
and $$D=C^T$$
and $$F=beginbmatrix G&H \I &Jendbmatrix$$
where $$G=beginbmatrix 8 &1&1&1\1&8&1&1\1&1&8&1\1&1&1&8endbmatrix$$ and $$H=beginbmatrix 0\0\0\0endbmatrix$$ and $$I=H^T$$ and
$$J=beginbmatrix 5endbmatrix$$
Show that $8$ is an eigen value of the matrix $A$.
How should I try to prove it?Please give some hints .I dont want a complete solution
linear-algebra matrices eigenvalues-eigenvectors
asked Aug 23 at 3:39
PureMathematics
976
asked Aug 23 at 3:39
PureMathematics
976
asked Aug 23 at 3:39
PureMathematics
976
asked Aug 23 at 3:39
PureMathematics
976
976
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
5
down vote
Hint:
- Examine the first two rows of $A-8I$, they are identical, what can you conclude.
Same result holds if you replace $D$ and $F$ with other matrices of the same size.
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
Hint:
- Examine the first two rows of $A-8I$, they are identical, what can you conclude.
Same result holds if you replace $D$ and $F$ with other matrices of the same size.
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
add a comment |Â
up vote
5
down vote
Hint:
- Examine the first two rows of $A-8I$, they are identical, what can you conclude.
Same result holds if you replace $D$ and $F$ with other matrices of the same size.
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
add a comment |Â
up vote
5
down vote
up vote
5
down vote
Hint:
- Examine the first two rows of $A-8I$, they are identical, what can you conclude.
Same result holds if you replace $D$ and $F$ with other matrices of the same size.
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
Hint:
- Examine the first two rows of $A-8I$, they are identical, what can you conclude.
Same result holds if you replace $D$ and $F$ with other matrices of the same size.
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
answered Aug 23 at 3:53
Siong Thye Goh
80.5k1453101
80.5k1453101
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
add a comment |Â
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
How to find the multiplicity,can you help
– PureMathematics
Aug 23 at 5:12
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
compute the nullity of $A-8I$, that is the multiplicity.
– Siong Thye Goh
Aug 23 at 5:18
add a comment |Â
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