Consider the 2 × 2 diagonal matrix A-[% 3] Then it is apparent that an A" hn for each integer n 2 1.

Q: find an elementary matrix E that satisfies the given equation EC = D

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Q: For matrix A, B if A – B = O, where O is a null matrix then * A = B B = 0 A = 0

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Q: If A is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: Let A, B, C be n x n matrices. Verify that (a) A is similar to A. (b) If A is similar to B and B is…

A: Given A, B, C be n × n matrices

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: Find the elementary matrix E such that EC A where [2 4. 2 -1 2. -2 and C = 4 A 2 -1 -2 8 -6 [16 10 E…

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Q: In the Attached Problem, show that the matrix A is nilpotent and then use this fact to find the…

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Q: find an elementary matrix E that satisfies the given equation EA = B

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Q: Let A be an n × n matrix. Is it possible for A2+I = O in the case where n is odd? Answer the same…

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Q: snip

A: Given, A=abcdD=ad-bc≠0

Q: If A is any matrix, to what is tr (AA T) equal?

A: Let A=[aij] be n X n matrix. Then  AT=[a'ij] where a'ij=aji Let C=AAT=[cij] , where

Q: find an elementary matrix E that satisfies the given equation E C =A

A: EC = A ECC-1 = AC-1 Hence, E = AC-1

Q: Let A = C 1. and X be a matrix satisfying: 2XT-A = (X + 2B)". B Then X is equal to the above equal…

A: The given problem is to find the matrix X which satisfies given matrix equation with given matrices.…

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

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Q: Find the echelon form of this augmented matrix, written so there are 1's on the diagonal. 1 -2 100…

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Q: In the Attached Problem, show that the matrix A is nilpotent and then use this fact to find the…

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Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: One of the following is not an elementary matrix 100 a) 010 b) 0 60 00 1 00 1 [100 00 1 c) 01 2 d)…

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Q: We will define a checkharel matrix to be a Square matrix A = (d), where di; = { 1 if it; is even Lo…

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Find diagonal matrix for given matrix by using formula: D= cAC [1 = To -2 A 2 -2 N O

A: The given matrix is, In the formula, D=C-1AC, the matrix C is the matrix of eigenvectors. The…

Q: 4 For matrix A = if g(X) = X2 + 4x + 2, what is the answer to g(A)? 3

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Q: If A is an n×n matrix with Col A​ =Rn​, how many solutions will there be to Ax​=b​, for any b in…

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Q: Given the matrix      A=       [4 -1   0   2] , then the trace of A^3 is?

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Q: If A is a 4×6 matrix and the dim Nul A​=3,what is dim Col A​? Justify your answer.

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Q: If A is a 2 x 3 matrix and the sum A + B can be computed, what is the size of B?

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Q: Show that if C and D are n×n row equivalent matrices, and Cx=0 has a non-trivial solution x !=0,…

A: Given that C and D are row equivalent matrices such that the system Cx=0 has a non trivial solution…

Q: (a) Given A E C"xn, for n e N, state the definition of the matrix exponential function exp(·A).

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Q: a) If a n x (n + 5) matrix has rank n, find dim Nul A, dim row A and rank A".

A: Given n=2 Matrix A is 2×7 matrix  We need to find dim(Nul A) ,dim(row A) and rank AT

Q: If A is a 4 x 6 matrix and the dim Nul A​=3, what is dim Col A​?  Justify your answer.

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Q: Apply the Gauss-Jordan method to invert the matrix given below. [1 0 0 01 1 1 0 0 1 1 0 L1 3 3 1 P =…

A: P=1000110012101331 is the given matrix to apply the Gauss-Jordan method on it that is RREF(Reduced…

Q: Tind the QR factorization of the given matrix. -1 1. 7 5 1 -1 1 1 -5

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Q: Given the matrix 1

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Q: メ-E to to L-E 2-E to to to d-E put K-E =U E= d-fX

A: The solution to the given question is explained below.

Q: Let A, B, C be n x n matrices. Show that if A is similar to B and B is similar to C, then A is…

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Q: For each of the following pairs of matrices, find an elementary matrix E such that EA = B

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Q: If D is an n × n diagonal matrix, how do the valuesof ||D||1, ||D||2, and ||D||∞ compare? Explain…

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Q: Let A be an n ×n matrix and B= A + I, where / is the identity matrix, then it is possible for A and…

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Q: Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but…

A: If  the dimension of the column space of  A will be 3  (or if A has set of three linearly…

Q: find an elementary matrix E that satisfies the given equation ED = C

A: Let the given matrices are, Give that ED=C

Q: Suppose that A is a 3 x 3 matrix. For each of the question (a)-(d), find the elementary matrix E…

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Q: If A E Mpx, (C) nXn is a square matrix, and B is unitarily similar to А, then A and В have the same…

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Q: Find both the sum and difefrence of Matrix A and В. (1 2 -1 '-s 5 9 k) A=0 1 2 B= 2 10 -9 4 2 -3) 6.…

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Q: If D is a 10 x 10 diagonal matrix with D5.5 = 2 (the entry in row 5 and column 5 of D), then what is…

A: The solution is given as follows :

Q: Let B be a Sx5 matrix and Caa): (a-1)(X-メーい(メ) Than the rann of 21-B is? A)S B) 4 c) 3 D) can't…

A: Rank of any matrix is equal to number of non zero rows of matrix when it is in row reduced echelon…

Q: (2 1) LA 3 4/

A:

Q: One of the following is not an elementary matrix 100 100 a) 00 1 b) 0 -5 0 020 0 0 1 104 001 c) 010…

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Q: Given that A is a 1 x 7 matrix and B is a 5 x 1 matrix. (a) Is AB defined? If so, what is the order…

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Q: If A is a 6×1 matrix and the sum A+B can be computed, what is the size of B?

A: Matrix addition. If A and B are matrices of the same size, then they can be added. (This is similar…

Q: For a 2 x 2 matrix A a |A| = d|

A: For the given 2 by 2 matrix A, a is multiplied by d and b is multiplied by c .

Q: Give the value(s) of a for which the columns in the matrix 8. -4 4 A = -4 +а 5 -6 4 -6 10 + a are…

A: We will find out the required values.

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.