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3 years ago

Identify each matrix A such that A^2 has identical diagonal elements?

Mathematics

1 answer:

Maksim231197 [3]3 years ago

6 0

Answer:

The correct matrices are:

Matrix:

7 1 5

1 5 7

5 7 1

all diagonal elements of A^2 are: 7^2 + 1^2 + 5^2

Matrix:

9 18 27

27 -9 18

18 27 9

all diagonal elements of A^2 are: 9^2 + 27*18 + 18*27 or (-9)^2

Matrix:

8 1 6

6 8 1

1 6 8

all diagonal elements of A^2 are: 8^2 + 6*1 + 1*6

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There are 10 marbles in a bag. Four are blue, 3 are black and 2 white and 1 red. If the marbles are not replaced once they are d

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Given:

Given that there are 10 marbles in a bag. 4 are blue, 3 are black, 2 are white and 1 is red.

The marbles are selected by not replacing the drawn ones.

We need to the probability of selected a black marble and then a white marble without replacement.

Probability:

Let B denote the black marble.

Let W denote the white marble.

The probability of selecting a black marble is $P(B)=\frac{3}{10}$

The probability of selecting a white marble without replacement is $P(W)=\frac{2}{9}$

The probability of selecting a black marble and then a white marble without replacement is given by

$P(B \ and \ W)=P(B) \cdot P(W)$

Substituting the values, we get;

$P(B \ and \ W)=\frac{3}{10} \cdot \frac{2}{9}$

$P(B \ and \ W)=\frac{6}{90}$

$P(B \ and \ W)=\frac{1}{15}$

Thus, the probability of selecting a black marble and then a white marble without replacement is $\frac{1}{15}$

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