Write Bold x as the sum of two vectors, one in Span StartSet Bold u 1 comma Bold u 2 comma Bold u 3 EndSet and one in Span Star
tSet Bold u 4 EndSet. Assume that StartSet Bold u 1 comma ... comma Bold u 4 EndSet is an orthogonal basis for set of real numbers R Superscript 4. Bold u 1equalsStart 4 By 1 Table 1st Row 1st Column 0 2nd Row 1st Column 1 3rd Row 1st Column negative 7 4st Row 1st Column negative 1 EndTable , Bold u 2equalsStart 4 By 1 Table 1st Row 1st Column 6 2nd Row 1st Column 8 3rd Row 1st Column 1 4st Row 1st Column 1 EndTable , Bold u 3equalsStart 4 By 1 Table 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column 1 4st Row 1st Column negative 7 EndTable , Bold u 4equalsStart 4 By 1 Table 1st Row 1st Column 8 2nd Row 1st Column negative 6 3rd Row 1st Column negative 1 4st Row 1st Column 1 EndTable , Bold xequalsStart 4 By 1 Table 1st Row 1st Column 12 2nd Row 1st Column negative 7 3rd Row 1st Column 2 4st Row 1st Column 0 EndTable
Verify that
StartSet Bold u 1 comma Bold u 2 EndSetu1,u2
is an orthogonal set, and then find the orthogonal projection of y onto
SpanStartSet Bold u 1 comma Bold u 2 EndSetu1,u2.
yequals=left bracket Start 3 By 1 Matrix 1st Row 1st Column 4 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix right bracket
4
2
−1
, Bold u 1u1equals=left bracket Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column 4 3rd Row 1st Column 0 EndMatrix right bracket
3
4
0
, Bold u 2u2equals=left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column 3 3rd Row 1st Column 0 EndMatrix right bracket
−4
3
0
Verify that
StartSet Bold u 1 comma Bold u 2 EndSetu1,u2
is an orthogonal set, and then find the orthogonal projection of y onto
SpanStartSet Bold u 1 comma Bold u 2 EndSetu1,u2.
yequals=left bracket Start 3 By 1 Matrix 1st Row 1st Column 4 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix right bracket
4
2
−1
, Bold u 1u1equals=left bracket Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column 4 3rd Row 1st Column 0 EndMatrix right bracket
3
4
0
, Bold u 2u2equals=left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column 3 3rd Row 1st Column 0 EndMatrix right bracket
−4
3
0
1 answer:
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Answer:
Step-by-step explanation:
You have the domain. It is given as -1≤x≤1
Now all you have to do is figure out the range which is the y value. At first glance I think it might be 3, but that does not look very logical. I'll post this much of it now and be back in under an hour with a more complete answer.
Of course! How silly of me. There is a minimum of y = 1 in the range which comes from x = 0
I've included a graph so you can see how this all works.
So the range = 1 ≤ y ≤ 3
The greatest whole possible whole number length of the unknown side is 9 inches.
<h3>How to identify if a triangle is acute?</h3>Let us have:
H = biggest side of the triangle
And let we get A and B as rest of the two sides.
Then we get:
If
then the triangle is acute
Two sides of an acute triangle measure as 5 inches and 8 inches
The length of the longest side is unknown.
We have to find the length of the unknown side
WE know that the longest side of any triangle is a hypotenuse
For an acute triangle we know:
Here in this sum,
a = 5 inches
b = 8 inches
c = ?
Substituting we get,
c < 9
Hence, The greatest whole possible whole number length of the unknown side is 9 inches.
Learn more about angles;
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