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2 years ago

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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Prove that sin²∅+cos²∅=1 ?

sasho [114]

Step-by-step explanation:

Let ABC be a right angled triangle where there's a right angle in B . Let the measure of the angle BAC be ∅. So,

$\sin(∅) = \frac{BC}{AC}$

$= > {\sin}^{2}∅ = \frac{ {BC}^{2} }{ {AC}^{2} }$

Also,

$\cos(∅) = \frac{AB}{AC}$

$= > { \cos}^{2}∅ = \frac{ {AB}^{2} }{ {AC}^{2} }$

Now adding the values of sin^2∅& cos^2∅,

${ \sin}^{2} ∅ + { \cos}^{2} ∅ = \frac{ {BC}^{2} }{ {AC}^{2} } + \frac{ {AB}^{2} }{ {AC}^{2} }$

$= > { \sin}^{2} ∅ + { \cos}^{2} ∅ = \frac{ {AB}^{2} + {BC}^{2} }{ {AC}^{2} }$

But we know that

${AC}^{2} = {AB}^{2} + {BC}^{2}$ by applying Pythagorean Theorem

So ,

$= > { \sin}^{2} ∅ + { \cos}^{2} ∅ = \frac{ {AC}^{2} }{ {AC}^{2} } = 1$

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2 years ago

Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digit

schepotkina [342]

Answer:

Y: 2

E: 9

A: 1

R: 0

Step-by-step explanation:

If we used the value Y = 2, E = 9 , A = 1 and R = 0

in the given equation i.e

$YYYY - EEE + AA - R = 1234$ .

From LHS,

Putting the value of Y,E, A and R in the given question we get

$2222-999+11-0\\=\ 1223\ + 11\\=\ 1234$

=RHS

$Therefore\ the\ value\ of \ Y, E, A, R\ is\ 2\ , \ 9 , \ 1\ and\ 0$

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3 years ago

5x - 6 = 3x - 8 what is the answer pls

marishachu [46]

The answer is x = - 1 i am positive

7 0

3 years ago

Read 2 more answers

Can anyone please help me

Dima020 [189]

don't

stay in school kids please don't

5 0

2 years ago

Really need some help

Viefleur [7K]

The outer exponent is 4 so there will be 5 terms all together. By rules of exponents

C(4,0)(3^4)(2^0)(x^8)(y^0) + C(4,1)(3^3)(2^1)(x^6)(y^3) + C(4,2)(3^2)(2^2)(x^4)(y^6) + C(4,3)(3^1)(2^3)(x^2)(y^9) + C(4,4)(3^0)(2^4)(x^0)(y^12)

The coefficient of the 3rd term: C(4,2)(3^2)(2^2) = 6 x 9 x 4 = 216

3 0

3 years ago