Answer with Step-by-step explanation:
We are given that two matrices A and B are square matrices of the same size.
We have to prove that
Tr(C(A+B)=C(Tr(A)+Tr(B))
Where C is constant
We know that tr A=Sum of diagonal elements of A
Therefore,
Tr(A)=Sum of diagonal elements of A
Tr(B)=Sum of diagonal elements of B
C(Tr(A))=
Sum of diagonal elements of A
C(Tr(B))= Sum of diagonal elements of B
Tr(C(A+B)=Sum of diagonal elements of (C(A+B))
Suppose ,A=![\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
B=![\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
Tr(A)=1+1=2
Tr(B)=1+1=2
C(Tr(A)+Tr(B))=C(2+2)=4C
A+B=![\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]+\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D)
A+B=![\left[\begin{array}{ccc}2&1\\2&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C2%262%5Cend%7Barray%7D%5Cright%5D)
C(A+B)=![\left[\begin{array}{ccc}2C&C\\2C&2C\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2C%26C%5C%5C2C%262C%5Cend%7Barray%7D%5Cright%5D)
Tr(C(A+B))=2C+2C=4C
Hence, Tr(C(A+B)=C(Tr(A)+Tr(B))
Hence, proved.
Answer:
(x, y) = (0, 1)
Step-by-step explanation:
For polar coordinates (r, θ), the corresponding rectangular coordinates are ...
(x, y) = (r·cos(θ), r·sin(θ))
For r=1 and θ=π/2, the rectangular coordinates are ...
(x, y) = (1·cos(π/2), 1·sin(π/2))
(x, y) = (0, 1)
The greatest common divisor of these numbers is 12.
Answer:
Step-by-step explanation:
Here you go mate
Use PEMDAS
Parenthesis
Exponent
Multiplication
Division
Addition
Subtraction
Step 1
-3(x-2)=9 Equation/Question
Step 2
-3(x-2)=9 Remove parenthesis
3x+6=9
Step 3
3x+6=9 Add -6
-3x=3
Step 4
−3x=3 Divide
answer
x=-1
Hope this helps
Answer:
10
Step-by-step explanation:
median is the middle number
these numbers in order are 2, 5, 6, 8, 12, 15, 19, 22 and the middle numbers are 8 and 12
to ind the middle number of those two numbers, you find the mean (averge) of those numbers
mean: 8+12=20/2=10
lmk if its right!
