Answer:
1 possibility is there for the the position of the fourth vertex.
Answer:
the answer is D.
Step-by-step explanation:
multiply each row in the first matrix by each column in the second matrix.
[4*-2+2*7 4*5+2*-1]
simplify each element of the matrix by multiplying out all the expressions.
[6 18]
this matrix is already in the most simplified form.
[6 18]
Answer:
a) ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
b) therefore Basis of W is
={ ![{\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
}
Step-by-step explanation:
Given the data in the question;
W = { A| Air Skew symmetric matrix}
= {A | A = -A^T }
A ; O⁻ = -O⁻^T O⁻ : Zero mstrix
O⁻ ∈ W
now let A, B ∈ W
A = -A^T B = -B^T
(A+B)^T = A^T + B^T
= -A - B
- ( A + B )
⇒ A + B = -( A + B)^T
∴ A + B ∈ W.
∝ ∈ | R
(∝.A)^T = ∝A^T
= ∝( -A)
= -( ∝A)
(∝A) = -( ∝A)^T
∴ ∝A ∈ W
so by subspace, W is subspace of 3 × 3 matrix
A ∈ W
A = -AT
A = ![\left[\begin{array}{ccc}o&a&b\\-a&o&c\\-b&-c&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Do%26a%26b%5C%5C-a%26o%26c%5C%5C-b%26-c%260%5Cend%7Barray%7D%5Cright%5D)
= ![a\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right]](https://tex.z-dn.net/?f=a%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%260%5C%5C-1%260%260%5C%5C0%260%260%5Cend%7Barray%7D%5Cright%5D)
![+b\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%5C%5C0%260%260%5C%5C-1%260%260%5Cend%7Barray%7D%5Cright%5D)
![+c\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%2Bc%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%260%5C%5C0%260%261%5C%5C0%26-1%260%5Cend%7Barray%7D%5Cright%5D)
therefore Basis of W is
={ }
-2y-4=4y-4
2) cancel 4 out on both sides
-2y=4y
3) divide both sides by -2
y=-2y
4) subtract both sides by -2y
y+2y=0
5)3y=0
6) divide by 3
Y=0
Answer:
Step-by-step explanation:
problem 4
Velocity is +2.0m/s and constant acceleration is -0.5m/s^2
For every second the velocity drop by 0.5 m/s, so after 2 seconds the velocity is 1 m/s.
problem 5
Accelerate from rest to 28m/s means go from 0 to 28m/s so with
a constant acceleration of 5.5 m/s^2 it will take 5.09 second
