(5) Let A, B be an n x n matrices. Explain why each of the following statements is true. (a) If B is row equivalent to A and det (B) 0, then det(A) 0 (Hint: use elementary matrices) (b) If A is not invertible, then A is row equivalent to a matrix with a zero row (c) If A is not invertible, then det(A) 0

Q: [2 8) Use the Gauss-Jordan method to find the inverse of the matrix A: %3D

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Q: An nx n matrix A is invertible if and only if it is row equivalent to I. O True O False

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Q: An mxn upper triangular matrix is one whose entries below the main diagonal are zeros, as is shown…

A:

Q: Is this statement true? It is possible for the square matrix A to be invertible and to have its…

A: Note: The determinant of a square matrix A indicates whether A is invertible or not.Now, det(A)=0 if…

Q: Consider an 5 x 5 matrix A satisfying the following two properties: (a) Every row has exactly one…

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Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

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Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: (0) Construct two non-zero 3x3 matrices A and B such that for A its rank is greater than its nullity…

A: two non-zero 3×3 matrices A and B such that for A its rank is greater than its nullityand for B…

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

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Q: -6 2 Show that A = and B = 9 -3 are similar matrices by finding an invertible -3 -1 -15 matrix P…

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Q: In the matrix equation (3A + XB) T = - (2X) T + B matrices A, B and X are matrices of Adequate…

A: Given, 3A+XBT=-2XT+B By right distributive law, 3AT+XBT=-2XT+B Rearranging the above equation we…

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

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Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: The matrix is not invertible for what value of x 2 1 1 1 31

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Q: An n x n matrix A is invertible if and only if it is row equivalent to I. 'n' O True O False

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Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: 3. Determine whether the matrix is elementary. If it is an elementary matrix, state the elementary…

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Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

A: Solution

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: 6. If A is a 4 x 2 matrix and B is a 3 x 2 matrix, what is the size of ABT?

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Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: A matrix A is similar to matrix B, if for some invertible matrix P, B = P''AP. Is B similar to A?

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Q: Let A be a 4 × 4 real symmetric matrix witheigenvaluesλ1 = 1, λ2 = λ3 = λ4 = 0 What type of matrix…

A: Given, A is a 4×4 real symmetric matrix with eigenvalues 1, 0, 0, 0. Now we have to find what is the…

Q: 1. Find an example of a 2 x 2 matrix A such that A² # I2, A³ + I2, and A® = I2. Explain how you…

A: Given that  a 2×2 matrix A such that A2≠I2,  A3≠I2 and  A6=I2

Q: 3. Is the trace of the product of two square matrices equal to the product of these two matrices'…

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Q: Let A, B, and C be invertible matrices. Then (4C2BTA-1)-1 is equal to 글A(BT)-1C-2 None of the…

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Q: Which is the matrix inverse to the matrix 2 3 1 3 2 1 1 0 1

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Q: Show that the matrix 2 1 A = 1 3 2 1 1 1 is invertible, but that A cannot be written as the product…

A: Solve the given problem.

Q: Let A, B, and C be invertible matrices. Then (4A-1B"C²)-1 is equal to c--(B")-1A equal to the above…

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Q: 2 Compute the inverse of the matrix A = -2 1 0. . Type DNE if A is not 3. invertible.

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Q: 4. A matrix A is similar to matrix B, if for some invertible matrix P, B = P'AP. Is B similar to A?

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Q: Show that the matrix is not diagonalizable.

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Q: Find the value of x so that the matrix is not invertible. 1. 3 2 0 [ 1 2 1 If answer is in decimal,…

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Q: -1 1 Verify that the matrix A = 3 is diagonalizable; 4 -2 5

A: We will use condition for matrix to be diagonalizable

Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: True or False If A and B are n × n lower triangular matrices, then AB is also lower triangular

A: Given, A and B are n×n lower triangular matrices. Consider 2×2 lower triangular matrix A=a0bc…

Q: Let A and B be n x n matrices.  Suppose that AB = On where On is a zero matrix of size n x n, and A…

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Q: 2.2.8 Show that if a matrix is positive definite then it is invertible, and its inverse is also…

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: A is a matrix of size 2x4, B is a matrix of size 3×2 Cis a matrix of size 2×4 D is a matrix of size…

A: Given: So, BT is a matrix of size 2x3, CT is a matrix of size 4x2, and DT is a matrix of size 3x4.…

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: We have to check whether given statement is true or false.

Q: Let A be an invertible, n x n matrix such that A² = A. a) Calculate det(A). b) If n = 3, what is A?…

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Q: 1) Answer TRUE or FALSE to the following questions. Provide a detailed argu- ment for your choice in…

A: Let A and B be n×n row equivalent matrices. If A is invertible, then B cannot be invertible.

Q: An n x n matrix A is invertible if and only if it is row equivalent to I. O True False

A: Given statement is "An n×n matrix A is invertible if and only if it is row equivalent to In."

Q: An mxn upper triangular matrix is one whose entries below the main diagonal are zeros, as is shown…

A: The solution is given as

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: Solution

Q: 4. (a) Prove that if A is an n x n invertible matrix that satisfies the equation A2 = A then A is…

A: Given [A] is n×n invertible matrix.  And satisfies A2 = A a) To prove [A] is an identity matrix b)…

Q: Example:1 Verify Cayley-Hamilton theorem for the matrix A= .2 41 and find its inverse. 3.

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.