An n x n matrix A is orthogonal if AA" = I. If A is orthogonal show that det(A) = ±1.

Q: a Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A: E=1k01  A=abcd

Q: Give the matrix X such that -1 -1 3. -2 X = 0. -5 Type DNE 4. -5 1 0. 0. if such a matrix does not…

A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: Q5. Show that the function from R"xn to R given by ||4||max = max |a¡j| i,j is not a norm by stating…

A: Given: A function from ·max : ℝn×n→ℝ defined by, Amax = maxi, jaij

Q: Find the standard matrix for the reflection T of R³ on the line , = . Your work must be shown! Is T…

A: We will first take an arbitrary point (x,y,z) then calculate its reflection point (x',y',z') about…

Q: Under what conditions will the diagonal matrix be invertible? Assume that A is invertible and find…

A:

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…

A:

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

A:

Q: IF A is a nonzero n X n matrix such that A 0, then A is singular. %3D Select one: True False

A:

Q: If the Reduced echelon form of A-λI is the identity matrix then what is the eigenspace (Eλ)?

A: We need to find the eigenspace (Eλ) if the Reduced echelon form of A-λI is the identity matrix. Note…

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

A:

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: Is it true or false? If A is nxn matrix, c is scalar, then cA |=c | A| Birini seçin:

A:

Q: Determine whether th e given matrix is orthogonal. If it is, find its inverse

A:

Q: Let A be 5x5 matrix. Which of the following criteria will ensure that A is diagonalizable over real…

A: Given A is a 5x5 matrix. We want to find criteria which ensure that A is diagonalizable.

Q: [2ß ß Find all the values of the parameter ß for which the matrix is 3 5B] Consider invertible.

A: The matrix is given as , A=2ββ35β find all values of β for which the matrix is invertible.

Q: Suppose that T() and 7 () -E Find the standard matrix A for Tand find T(:) 14 and 2 and T (HD A-3…

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Q: ind the spectral radius of the matrix T; of Jacobi method for the following lineer system: 1+3X3=2,…

A:

Q: Suppose that x and y are mxn matrices. Prove that xT- yT=(X -YT. Find a 2x2matrix A, that is not the…

A: Take A and B as arbitrary m×n matrices and evaluate the left and right sided expression

Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

A:

Q: A = (ai j )is a 3 × 3 matrix, develop the general ex-pression for det(A) by expanding(a) along the…

A: Given: Let A=aij be a 3×3 matrix.  To determine: The general expression for det(A) by expanding  a)…

Q: A n x n Hermitian matrix contains exactly k real entries. Show that k + n must be even.

A:

Q: Let A be a m times nm×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b…

A: Let A be an m×n matrix such that Ax​=b and Ax​=c each have a solution for some choice of b and c in…

Q: What is 'a', if B as shown below is a singular matrix?

A: A singular matrix is a matrix whose determinant is zero.

Q: compute e^At and e^-At of an identical matrix,I (1  0  0  1)

A:

Q: If A is 3 x 3 matrix such that (A + I3)² = 0 %3D Show that: A is invertible.

A:

Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

A:

Q: If A is an invertible n X n matrix, show that adj A is also invertible

A: Given: To Prove: Concept: 1. 2.

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

A:

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: Let A be an m × n matrix of rank n and let P =A(ATA)−1AT . If b ∈ R(A)⊥, show that Pb = 0.

A:

Q: Verify by finding the matrix of S 0 T (a) by direct substitution and (b) by matrix multiplication of…

A:

Q: Let Q be an m xn matrix with n >n and orthonormal columns, then we have both QTQ = I, and QQT = Im…

A:

Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

A:

Q: Find value(s) of ß for which the matrix A is singular. —3 - в |-2 B 1 1

A: Given:         A=β-3-β-2β1β10    A matrix is singular if and only if the determinant of a matrix is…

Q: Assume that A and B are both n x n matrix. If|AB| + 0, then both A and Bare invertible. O True O…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let  A be a symmetric tridiagonal matrix (i.e., A is symmetric and aij = 0 when ever |i−j| > 1). Let…

A:

Q: 2. Q is an xn symmetric matrix, b is a vector of size n and c is a scalar If f(x) = x"Qx + b"x + c:…

A: given  fx=12xTQx+bTx+c it is known that  gradient of the function can be expressed as…

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

A:

Q: Let A E Mn(C) denote the n x n matrix with all entries equal to 1. Show that A is positive…

A: Let A belongs to  Mn (C) denote the n x n matrix with all entries equal to 1. Show that A is…

Q: In all parts, suppose that A is a matrix of size 11 x 8 (i) Assuming that rank(Atr) = 3, determine…

A: It is given that

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?…

A:

Q: Let A = 3 0 -1 2 Compute the indicated matrix. (If this is not possible, enter DNE in any single…

A: Solve  for the A^3

Q: Let 6 A = E = F = 4 2 Compute the indicated matrix. (If this is not possible, enter DNE in any…

A:

Q: Let A be a mxn matrix that n > m (a) Explain why A = 0 has at least a non-trivial solution. %3D

A: (a) Given that A is an m×n matrix. The objective is to explain why Ax=0has non trivial solution.…

Q: Given two m ×m matrix X and Y , where XY = Y X. 1) Let u be an eigenvector of X. Show that either Y…

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Q: a b Verify that det EA = (det E)(det A), where E is the elementary matrix shown and A =

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.