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elena55 [62]
3 years ago
7

Frorn first to last, when did the presidents serve?

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0

Step-by-step explanation:

you got this i believe in you

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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
Suppose a circle with center (14,9) passes through point (16, 12). Which equation represents the circle?
kifflom [539]

Answer:

( x - 14)^2 + ( y - 9)^2 = 13

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( 14 , 9) - center-( a, b)

a = 14

b = 9

( 16 , 12) - point - ( x, y)

x = 16

y = 12

Step 1: substitute the center into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

Step 2: substitute the point into the equation

( x - 14)^2 +( y - 9)^2 = r^2

( 16 - 14)^2 + ( 12 - 9)^2 = r^2

2^2 + 3^2 = r^2

4 + 9 = r^2

13 = r^2

Step 3: subs the radius into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

( x - 14)^2 + (y - 9)^2 = 13

Therefore, the equation of the circle is

( x - 14)^2 + ( y - 9)^2 = 13

8 0
3 years ago
Write 8/74 in simplest form.
WINSTONCH [101]
The answer is C 8/2=4 and 74/2=37
7 0
3 years ago
Read 2 more answers
Mary bought a 7lb bag of flour. She used 1/3 of the bag to bake wedding treats.
oee [108]

Answer:

she is left with 4.67 LB of flour.

Step-by-step explanation:

7 divided by 3 = 2.3333333

2.3333333 x 2 = 4.67

8 0
2 years ago
Solve for k.<br>7k - 2 ≥ -9​
Akimi4 [234]

Answer: k ≥ -1

Step-by-step explanation:

7k - 2 ≥ -9

add two to both sides

7k ≥ -7

k ≥ -1

6 0
3 years ago
Read 2 more answers
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