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dem82 [27]
2 years ago
9

Is matrix multiplication comutative?

Mathematics
1 answer:
konstantin123 [22]2 years ago
6 0

Answer:

Matrix multiplication is not conmutative

Step-by-step explanation:

The matrix multiplication can be performed if the number of columns of the first matrix is equal to the number of rows of the second matrix

Let A with dimension mxn and B with dimension nxp represent two matrix

The multiplication of A by B is a matrix C with dimension mxp, but the multiplication of B by A is can't be calculated because the number of columns of B is not the number of rows of A. Therefore, you can notice that is not conmutative in general.

But even if the multiplication of AB and BA is defined (For example if A and B are squared matrix of 2x2) the multiplication is not necessary conmutative.

The matrix multiplication result is a matrix which entries are given by dot product of the corresponding row of the first matrix and the corresponding column of the second matrix:

A=\left[\begin{array}{ccc}a11&a12\\a21&a22\end{array}\right]\\B= \left[\begin{array}{ccc}b11&b12\\b21&b22\end{array}\right]\\AB = \left[\begin{array}{ccc}a11b11+a12b21&a11b12+a12b22\\a21b11+a22b21&a21b12+a22b22\end{array}\right]\\\\BA=\left[\begin{array}{ccc}b11a11+b12a21&b11a12+b12a22\\b21a11+b22ba21&b21a12+b22a22\end{array}\right]

Notice that in general, the result is not the same. It could be the same for very specific values of the elements of each matrix.

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6/11 is the simplest form of the fraction. 
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Step-by-step explanation:

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3 years ago
The change in water vapor in a cloud is modeled by a polynomial function, C(x). C(x) = x^3+ 5x^2+3x+30 Describe how to find the
kari74 [83]

Answer:

Suppose the equation that describes the change in water vapor in a cloud (y) with respect to temperature (x): C(x) = x³ - 4x² - 7x + 10

You find the x-intercepts of the cubic equation by finding the roots. Let y be zero:

x³ - 4x² - 7x + 10 = 0

Now, find possible factors of the constant term in the equation: 10. These could be 1, 2, 5, and 10. Suppose we choose 1. We substitute x=1. If the answer is zero, then x=1 is one of the roots.

(1)³ - 4(1)² - 7(1) + 10 = 0

Hence, x=1 or x-1 = 0 is one of the roots. We use this to manipulate the rest of the terms in the original equation, such that you can factor out (x-1). Substitute -x² - 3x² to -4x³ because they are just equal. Same is true for +3x - 10x for -7x:

x³ -x² - 3x²+3x - 10x + 10 = 0

Factor out like terms such that they have a common factor of (x-1) as much as possible.

x³ -x² = x²(x-1)

- 3x²+3x = -3x(x-1)

- 10x + 10 = -10(x-1)

The factored equation is:

x²(x-1)-3x(x-1)-10(x-1) = 0

Factor out (x-1):

(x-1)(x²-3x-10) = 0

Now, we have the quadratic equation left to be solved:x²-3x-10

Use the quadratic formula to find the roots:

x = [-b +/- √(b²-4ac)]/2a,

The a, b and c coefficients are based on the general form of the quadratic equation: ax² + bx + c. Hence, a=1, b=-3 and c=-10. Substituting the values:

x = [-(-3) +/- √((-3)²-4(1)(-10))]/2(1)

x = 5, -2

Therefore, the roots of the cubic equations are x = 1, x = 5 and x =- 2. These are the x-intercepts of the equation. At temperatures °C, 5°C and -2°C, there is no change in water vapor in a cloud. The graph is shown in the attached picture

Step-by-step explanation:

7 0
2 years ago
3(x+4) - (x-1)<br> x=3 y=2
Ksenya-84 [330]

Answer: 19

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Need Help Please!!!!!!!
marshall27 [118]

ANSWER

$1,413.81

EXPLANATION

The compound interest formula is given by:

A=P(1+r\%)^t

Where P=900 is the balance in the account, t=10 is the number of years and r=0.0462 is the rate.

We substitute the values in to the formula to get:

A=900(1+4.62\%)^{10}

A=900(1.0462)^{10}

This simplifies to:

A=1413.81

Therefore $1413.81 will be in the account after 10 years.

6 0
3 years ago
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