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-BARSIC- [3]
2 years ago
11

Simplify: (a4 - 6a + 5) - (a4 - 3a + 2a2 - 6)

Mathematics
1 answer:
Galina-37 [17]2 years ago
7 0
(a4-6a+5)-(a4-3a+4a-6)
by expressing like term
a4-a4=0
-6a-(-3a+4a)=-5a
5-(-6)=11
:we have-5a+11
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skew-symmetric 3 x 3 matrices form as subspace of all 3 x 3 matrices and find a basis for this subspace.
Neporo4naja [7]

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] ,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]}

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]

= a\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right] +b\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] +c\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]

therefore Basis of W is

={ {\left[\begin{array}{ccc}0&1&0\\-1&0&0\\0&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&1\\0&0&0\\-1&0&0\end{array}\right] ,\left[\begin{array}{ccc}0&0&0\\0&0&1\\0&-1&0\end{array}\right]}

8 0
3 years ago
What is the volume of the pyramid below?
igomit [66]

Answer:

12

Step-by-step explanation:

Base area = 3×4/2 = 6 ft²

height = 6 ft

volume = 6×6/3 = 12 ft³

Answered by GAUTHMATH

8 0
3 years ago
In parallelogram DEFG, DH equals X +3, HF equals 3Y, GH equals 2X -5 and HE equals 5Y plus to find the values of X and Y
daser333 [38]

The values of X and Y are 30 and 11 respectively

<h3>How to determine the values of X and Y?</h3>

The figure that represents the complete question is added as an attachment

The given parameters are:

DH = X +3

HF  = 3Y

GH = 2X -5

HE = 5Y

From the attached parallelogram, we have:

DH = HF

GH = HE

Substitute the known values in the above equation

X + 3 = 3Y

2X - 5 = 5Y

Make X the subject in X + 3 = 3Y

X = 3Y - 3

Substitute X = 3Y - 3 in 2X - 5 = 5Y

2(3Y - 3) - 5 = 5Y

Expand

6Y - 6 - 5 = 5Y

Evaluate the like terms

Y = 11

Substitute Y = 11 in X = 3Y - 3

X = 3*11 - 3

Evaluate

X = 30

Hence, the values of X and Y are 30 and 11 respectively

Read more about parallelograms at:

brainly.com/question/3050890

#SPJ1

8 0
11 months ago
By driving 8 mph faster than Bob, John can make a 230 mile trip in one half hour less. How fast does Bob drive on the trip? Roun
____ [38]

Answer: The speed of Bob is 56.8 km/hr.

Step-by-step explanation:

Let the speed of Bob be 'x'.

Let the speed of John be 'x-8'.

Distance covered = 230 miles

time = 1\dfrac{1}{2}=\dfrac{3}{2}\ hr

According to question, we get that

\dfrac{230}{x}-\dfrac{230}{x+8}=\dfrac{3}{2}\\\\230\dfrac{x+8-x}{x(x+8)}=\dfrac{3}{2}\\\\\dfrac{230\times 8}{x^2+8x}=\dfrac{3}{2}\\\\\dfrac{1840}{x^2+8x}=\dfrac{3}{2}\\\\1840\times 2=3x^2+24x\\\\3680=3x^2+24x\\\\3x^2+24x-3680=0\\\\x\approx 56.8\ km/hr

Hence, the speed of Bob is 56.8 km/hr.

6 0
3 years ago
Whats 1x500 plsssssssssssssssssss
Ivenika [448]

Its 500

because anything that is getting multiplied by one is the same number.

7 0
3 years ago
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