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Nat2105 [25]
3 years ago
14

True or false: (a) If A2 is defined then A is necessarily square. (b) If AB and BA are defined then A and Bare square. (c) If AB

and BA are defined then AB and BA are square. (d) If AB
Mathematics
1 answer:
andrew-mc [135]3 years ago
4 0

(a) True. Suppose A is a not a square matrix, with m rows and n columns. Then A² is not defined, because you can't multiply an m×n matrix by another m×n matrix.

(b) False. As an example, consider the matrices

A_{3\times2} = \begin{bmatrix}1&0\\0&1\\0&0\end{bmatrix}

B_{2\times3} = \begin{bmatrix}-1&0&1\\0&0&1\end{bmatrix}

Then both AB and BA are defined, with

AB_{3\times3} = \begin{bmatrix}-1&0&1\\0&0&1\\0&0&0\end{bmatrix}

BA_{2\times2} = \begin{bmatrix}-1&0\\0&0\end{bmatrix}

In general, you can multiply any m×n by any n×m matrix.

(c) True. Multiplying a m×n matrix by a n×m matrix always yields a m×m matrix, and multiplying a n×m matrix by a m×n matrix always yields a n×n matrix.

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Finding three volume is super easy the equation for volume is the area of the base times the height so u will find the area of all the small part and then add those and then multiply by the height
6 0
3 years ago
Pizzeria Napoli sells a round pizza with diameter 16 inches and a square pizza with side length 15 inches. Which of the two shap
zavuch27 [327]

Answer: Square, 24 square inches

Step-by-step explanation:

Given

Diameter of round pizza d=16\ in.

Side of square pizza a=15\ in.

Area of circle \pi r^2

The area of a square is a^2

\therefore \text{Area of round Pizza}=\pi \times (\frac{16}{2})^2\\\Rightarrow A_1=\pi \times 8^2=201.088\ in.^2

The area of square pizza is

A_2=15^2=225\ in.^2

Clearly, the area of square pizza is more and the difference in their area is

\Rightarrow A_2-A_1=225-201.088=23.91\approx\ 24\ in.^2

6 0
2 years ago
A rectangular plot of land has an area 9/10 square mile.The length is 3/2miles whats the width
Georgia [21]
A = L * W
(9/10) = (3/2) * W
Divide both sides (3/2)
(9/10) / (3/2) = W
(9/10) * (2/3) = W
18/30 = W
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6 0
4 years ago
Read 2 more answers
Show the work please
Kay [80]

Answer:

1) (x + 3)(3x + 2)

2) x= +/-root6 - 1 by 5

Step-by-step explanation:

3x^2 + 11x + 6 = 0 (mid-term break)

using mid-term break

3x^2 + 9x + 2x + 6 = 0

factor out 3x from first pair and +2 from the second pair

3x(x + 3) + 2(x + 3)

factor out x+3

(x + 3)(3x + 2)

5x^2 + 2x = 1 (completing squares)

rearrange the equation

5x^2 + 2x - 1 = 0

divide both sides by 5 to cancel out the 5 of first term

5x^2/5 + 2x/5 - 1/5 = 0/5

x^2 + 2x/5 - 1/5 = 0

rearranging the equation to gain a+b=c form

x^2 + 2x/5 = 1/5

adding (1/5)^2 on both sides

x^2 + 2x/5 + (1/5)^2 = 1/5 + (1/5)^2

(x + 1/5)^2 = 1/5 + 1/25

(x + 1/5)^2 = 5 + 1 by 25

(x + 1/5)^2 = 6/25

taking square root on both sides

root(x + 1/5)^2 = +/- root(6/25)

x + 1/5 = +/- root6 /5

shifting 1/5 on the other side

x = +/- root6 /5 - 1/5

x = +/- root6 - 1 by 5

x = + root6 - 1 by 5 or x= - root6 - 1 by 5

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3 years ago
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