Let A be an nxn matrix and B= A+I, where / is the identity matrix, then it is possible for A and B to be similar. Select one: True False

Q: If A and B are n × n diagonal matrices, show that AB = BA.

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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: Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix…

A: I assume you know what is an argument matrix and what is rank of matrix .

Q: Find x such that the matrix is equal to its own inverse. A = -5 -6

A: Given A=6X-5-6

Q: 6 4 (a) -1 2 -2 0 (b) 6 1 0 0 0 (c) 5 5 5 0 0 0 0 -1 -3 (d) 3 3 -2 1

A:

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

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Q: Let A= B = If possible, compute the following. If an answer does not exist, enter DNE. AB = help…

A: The given matrices are, A=24-3-3  and  B=35-14. Since both matrix are 2×2 square matrix, the matrix…

Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

Q: Write down the necessary conditions for the matrix B2*2 (2 ∗ 2 matrix) to have an inverse matrix.

A: Necessary conditions for a 2*2 matrix to have an inverse matrix.

Q: Identify that the given matrix is Diagonalisable or not: -2 = | -2 6

A: A matrix is said to be diagonalizable if it is similar to a diagonal matrix. Also, if a matrix has…

Q: Identify that the given matrix is Diagonalisable or not: -2 A = 2 6 -1 1 5.

A: It is diagonalisable

Q: Let A be a 4x6 matrix. what is the dimension of Col A if the nullity is 2? Explain

A: 4

Q: Give an example of a nonzero 2 X 2 matrix A such that A2=O

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

A:

Q: If A is a square matrix, then Ker(A) = Ker(RREF). True or false?

A: If A is aquare matrix then we have to check Ker(A) =Ker(RREF(A))

Q: If A is a 31x24 matrix whose rank equals 10, find dim(Nul(AT)). Your Answer:

A:

Q: An identity matrix is represented by... . а. Нн-1 O b. HH-H C. H-H

A: Given

Q: Let If A is 2x2 matrix and /(4)=0, then %3D

A:

Q: Find x such that the matrix is equal to its own inverse. A = -2 -5

A: Topic = Matrices

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

A:

Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: Let A be an mtimes×n matrix and let B be an ntimes×p matrix. If the first row of A consists only of​…

A:

Q: Let A and B be symmetric n × n matrices and let C = AB. Is C symmetric? Explain.

A:

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

A:

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, A = [6…

A: We have to find the inverse

Q: Find the inverse of the matrix by Gauss-Jordan Elimination (using an adjoined matrix). (If an answer…

A:

Q: If A is a symmetric matrix, does it follow that the transpose of matrix A is also symmetric?…

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Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

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Q: Determine whether the matrix is symmetric.

A:

Q: Let A be a 4 x 4 matrix with |adj(A) = -8, then 2A.adj(2A) - (where 1, is 4 x 4 identity matrix)…

A: Given that: A is a 4x4 matrix.                       |adj(A)|=-8

Q: Let A and B be n × n matrices and let C = A − B. Show that if Ax0 = Bx0 and x0 = 0, then C must be…

A: Consider the A and B are n×n matrices and C=A-B. If x0=0, Ax0 =0 and Bx0 =0 are nontrivial…

Q: Find the inverse of the matrix A, then prove that Ax A-1 =1, 3 -2 1) A =

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Q: Find x such that the matrix is equal to its own inverse.

A:

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 6 -2 -4…

A:

Q: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

A:

Q: I. State whether or not the given matrix is (a) upper triangular, (b) lower triangular, (c)…

A:

Q: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: Suppose A is a 10x10 invertible matrix. Then A is row equivalent to the 10x10 identity matrix. A)…

A:

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: Let A be a 3x3 matrix where A2=I3, then det(A) is 1 or -1. Select one: 1-True 2-False

A: To find- Let A be a 3×3 matrix where A2 = I3, then detA is 1 or -1. True False

Q: Let A be a 3x3 matrix where A?=13, then det(A) must be equal to 1. Select one: O True O False

A:

Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

A:

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.