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Alinara [238K]
3 years ago
6

Answer all questions please

Mathematics
1 answer:
Marat540 [252]3 years ago
4 0

Answer:

4.

a. base angle

b. leg

c. vertex

d. leg

e. base

f. base


5. You have 3 pairs of corresponding congruent sides, so the property that proves the triangles are congruent would be SSS.  



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Show that the sets of upper-triangular and lower-triangular matrices are subspaces of F n,n . Call them U and L respectively. Wh
soldi70 [24.7K]

Answer:

dim L = dim U = \frac{n(n+1)}{2}

Step-by-step explanation:

We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices A=(a_{ij}) such that the entry a_{ij}=0 if i<j.

Now let A=(a_{ij}) and B=(b_{ij}) be two lower triangular matrices, now if

C=A+\lambda  B for some \lambda \in \mathbb{F}

then the entry c_{ij} of C is equal to

c_{ij}=a_{ij}+\lambda b_{ij}

Now, if i<j, it must hold that a_{ij}=0 \quad \text{and} \quad b_{ij}=0. Therefore, if this is the case we must have that c_{ij}=0 and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.

To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of \mathbb{F}, any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,

\dimL=n+(n-1)+(n-2)+...+2+1=\dfrac{n(n+1)}{2}

5 0
3 years ago
What addition double fact can help you find 4+3? Explain how you know
cestrela7 [59]
3+4 because they are both the same answer
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Help me please ..........................................................
ale4655 [162]
It would be the last one to add up to 180 witch is a triangle or supplementary
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ASAP DINT ANSWER IF YOU DONT DO ALL BRAINLEST TO THE ORECT ANSWERS
KiRa [710]

Answer:

The first one towards the left, or the green triangle, would be 70 degrees.

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2 years ago
22.5+7(n-34) simplified
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