Answer:
−3x^8 + 9x^2 + 10x
Step-by-step explanation:
A polynomial is in standard form when the exponents of the variable decrease left to right. The only given expression in that form is ...
−3x^8 + 9x^2 + 10x
Answer:
2
Step-by-step explanation:
(7^1/2)^2=7^(1/2*2)=7
Answer:
(A) Set A is linearly independent and spans 
. Set is a basis for .
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors ![A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right)](https://tex.z-dn.net/?f=A%3D%20%5Cleft%28%5Cbegin%7Barray%7D%7B%5Bc%5D%5Bc%5D%5Bc%5D%5Bc%5D%7D1%20%26%200%20%26%200%20%26%200%5C%5C%200%20%26%201%20%26%200%20%26%201%5C%5C%200%20%26%200%20%26%201%20%26%201%5Cend%7Barray%7D%20%5Cright%29%20)
, we are to decide which of the given statements is true:
In Matrix ![A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right)](https://tex.z-dn.net/?f=A%3D%20%5Cleft%28%5Cbegin%7Barray%7D%7B%5Bc%5D%5Bc%5D%5Bc%5D%5Bc%5D%7D%281%29%20%26%200%20%26%200%20%26%200%5C%5C%200%20%26%20%281%29%20%26%200%20%26%201%5C%5C%200%20%26%200%20%26%20%281%29%20%26%201%5Cend%7Barray%7D%20%5Cright%29%20)
, the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans .
Therefore Set A is linearly independent and spans . Thus it is basis for .
Given:
Compound shape
To find:
The area of the compound shape.
Solution:
The compound shape is splitted into two parallelograms.
<u>Bottom parallelogram:</u>
Base = 7.5 cm
Height = 5 cm
Area of the parallelogram = base × height
= 7.5 × 5
= 37.5 cm²
The area of the Bottom parallelogram 37.5 cm².
<u>Top parallelogram:</u>
Base = 7.5 cm
Height = 4.5 cm
Area of the parallelogram = base × height
= 7.5 × 4.5
= 33.75 cm²
The area of the top parallelogram 33.75 cm².
Compound shape = 37.5 + 33.75
= 71.25 cm²
The area of the compound shape is 71.25 cm².
Answer:
324900
Step-by-step explanation:
