2. Every square matrix A can be decomposed as a product of three matrices A = SDR where S and R are invertible and D is diagonal.

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: If A is a square matrix such that A2 = 0, then A is invertible. True or false

A: A is a square matrix, so, det(AB) = det(A) det(B)

Q: CD, where C and D are n x n matrices and C is invertible. Prove that the matrix product DC is…

A:

Q: Compute the rank and nullity of the given matrices over the indicated Zp

A:

Q: .

A:

Q: Consider the Az 1 34 17 9 203 2 8 16 6 0 5 /

A: (a) We know that we can find the determinant of the matrix by expanding along any column or row.…

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

A:

Q: "Let A, B be n x n matrices. If 3A(B“) is invertible, then both A and B are invertible."

A:

Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A:

Q: Suppose that A and B are orthogonal (n x ) matrices. Show that AB is an orthogonal matrix.

A:

Q: Let A, B, and C be three nonzero n × n matrices such that AC = BC. Does it follow that A = B? If so,…

A:

Q: 4. Prove that if A is a square matrix, then det(A™ A) = det(AA") %3D

A:

Q: Show that A = 3 and B = are similar matrices by finding an invertible matrix P satisfying A = P-'BP.…

A: We are given two matrices A and B and we have to show that these are similar matrices.For this we…

Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: If the null space N(A) of a 5 xX 6 matrix A has dimension 4, what can you say about the dimension of…

A:

Q: Give the rank and the nullity of the matrices in the given exercise.

A: Given, A=11-30211-1-4 from rank nuility theorem we can say, ρA+ηA=dimA now find rank of A…

Q: Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is symmetric,…

A: Given that B=QRQ-1 where, Q is orthogonal and R is upper triangular. Then, multiply Q on both sides:…

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: Show that A = P-¹BP. [2-13] -4 and B = 1 -2 -2 2 are similar matrices by finding an invertible…

A: To show that          A=7-132-4, and   B=1-2-22 are similiar matrices.

Q: Let A, B and C be square invertible matrices of the same size. If BTB=I=BBT(XT is the transpose of…

A: A square matrix is said to be invertible if their inverse exists that is determinant of matrix is…

Q: Compute the rank and nullity of the given matrices over the indicated Zp

A:

Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

Q: 4. Suppose A is a nonsingular matrix with SVD A= UEV*.

A:

Q: Suppose that A € Mnxn(R) is a positive-definite symmetric matrix. Since A is symmetric, A is or-…

A: We will use the knowledge of standard value decomposition (SVD) of a square matrix.

Q: Suppose Q = PCP-1 where P is orthogonal, and C is upper triangular. Prove that if Q is symmetric,…

A:

Q: Prove that with gauss jordan! If A is an n squared matrix and if we can find a matrix B such that…

A:

Q: Let A and B be matrices with size 3 x 3. If only one of these matrices are diagonalizable and if…

A: Given, A and B be matrices with size 3×3det(A-λI3)=(λ-2)(λ2-9)det(B-λI3)=(λ-3)2(λ+2)(a) Eigenvalues…

Q: If A is a nonsingular matrix such that A2 = A, what is det(A)?

A: Given: A is a non-singular matrix such that A2=A. To find: A Solution: Non-singular matrix is a…

Q: a) compute det(A),det (B) b) Is the matrix A invertible? Why?

A:

Q: Suppose A and B are matrices with AB=0 (where 0 represents the zero matrix of the appropriate size).…

A:

Q: (3) The product A¡ A2 of two upper triangular matrices A1 and A2 is also upper triangular.…

A: Suppose A1 and A2 are the upper triangular matrices of order   such that   and where the diagonal…

Q: Suppose A-A, where A is the matrix. The det (A) is

A: Determinant of a null matrix is equal to zero.

Q: 7. Suppose U is an m x n matrix and V is an n x m matrix for which In-VU is invertible. Show that…

A:

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: If a is skew symmetric nxn matrix and n is odd,prove that det A = 0.

A: Consider a skew symmetric n x n matrix A where n is odd. Here the objective is to prove that det(A)…

Q: 0, then A is singular. IF A is a nonzero nX n matrix such that A Select one: True False

A:

Q: 1. For any 3x3 matrices A & B: Verify that (AB)" = B"A". %3D

A: By using the properties

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

A:

Q: Suppose that A is an invertible matrix with n columns, and entry aij in row i and column j. 1.…

A: Let matrix is A and the entries are aij .

Q: Suppose that A is an n × n matrix and det A + 0. Determine the rank and nullity of A.

A:

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: If an nxn matrix A is invertible, then the rowa of A' are linearly independent. T O True O False

A: If a matrix is invertible then its rows are linearly independent

Q: If the first two rows of a matrix A are equal and the matrix product AB is defined, then the first…

A:

Q: Suppose A is a 5x9 matrix and Rank(A) = 3. Find dim(null(A)-). O 1 3 O 6

A: Given; A is a 5*9 matrix and Rank(A)=3.

Q: Suppose A and I are bothn x n matrices, then

A:

Q: Suppose A, B, and C are three non-zero square matrices such that AC = BC. Is it true that A = B? If…

A: Not true

Q: If A is an invertible matrix and det(A) = 7, what is det (A-1)?

A: Given: If A is an invertible matrix and det(A) = 7 To find: what is det (A-1 )?

Q: If A is any invertible n x n matrix, then rref( A) In. %3D True False

A: Invertible matrices, An n×n matrix A is invertible if there exists an n×n matrix B such that…

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.