Select four statements from the invertible matrix theorem and show that all four statements are true or false
1 answer:
Answer:
A) A is an invertible matrix ( TRUE )
B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )
C ) The equation Ax = 0 has only the trivial solution ( TRUE )
D ) The columns of A form a linearly independent set ( TRUE )
Step-by-step explanation:
Assuming a matrix A
det A = 1 [ 0 -3 ] + 2 [12 + 5 ] + 1[-1]
= -3 + 34 -1 = 30 ≠ 0
THEREFORE det A = 30 ≠ 0
Attached is the detailed solution of the given statements above
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Answer:
(a1) The probability that temperature increase will be less than 20°C is 0.667.
(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.
(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.
(c) The expected value of the temperature increase is 17.5°C.
Step-by-step explanation:
Let <em>X</em> = temperature increase.
The random variable <em>X</em> follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].
The probability density function of <em>X</em> is:
(a1)
Compute the probability that temperature increase will be less than 20°C as follows:
Thus, the probability that temperature increase will be less than 20°C is 0.667.
(a2)
Compute the probability that temperature increase will be between 20°C and 22°C as follows:
Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.
(b)
Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:
Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.
(c)
Compute the expected value of the uniform random variable <em>X</em> as follows:
Thus, the expected value of the temperature increase is 17.5°C.