True or false? For each part, determine if you believe the statement is true or false, and justify your answers as appropriate. (a) If B is an m x n matrix with m

Q: (2) Determine all the real numbers a, b, c for which the matrix a 0 b 0 C is not diagonalizable.

A: The given problem is to determine for what values of a,b,c the matrix is not diagonalizable.

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not…

A:

Q: Find (a) the nullspace, (b) the nullity, and (c) the rank of the matrix A. Then verify that rank(A)…

A: It is given that,  A = 10-204-24-2-2013. a) Find the null space of A. b) Find the nullity of A. c)…

Q: Write the dot product of (1, 4, 5) and (x, y, z) as a matrix multiplication Ax. The matrix A has one…

A: Given, A=145, x=xyz Ax=0

Q: c. Find an orthogonal diagonalization of the symmetric matrix 1 -2 0 A = -2 1 4

A:

Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

A: A matrix is diagonalizable if A.m. of each eigen value = g.m. of corresponding eigen value

Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

A:

Q: Q2) In each of the following cases, find the matrix A for which [v]D=A[v]B a. B={1, 2x, 4x²-1} and…

A: Here we use the definition of the change of basis matrix. For that we first write the basis elements…

Q: Consider the following matrices: -7 M = -1 (4-2) and (NM) - (34) 2 7 T = 1 a) Find matrix N. b)…

A: Step 1: Step 2: Step 3: Step 4:

Q: For the matrix A, find an orthogonal matrix P such that P-1 A Pis diagonal. 3-2 41 A = I ده است مراد…

A:

Q: ) Let A, B be matrices with real coefficients. (a) Find A and B such that AB is defined and BA is…

A:

Q: Given the matrix 1 0 1 -1 1

A:

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

A:

Q: = 1 -2 2 00 0 -1 0 0 -1

A: Given that A=

Q: Find a 2 × 2 matrix that maps e₁ to -3e2 and e2 to 2e1–e2.

A: The 2x2 matrix that maps e1 to -3e2 and e2 to 2e1 - e2 is [02​−3−1​]Explanation:

Q: Properties of Transpose If r is a scalar and A and B are matrices of the appropriate sizes, then 1.…

A:

Q: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Let A be a 3x3 matrix. Show that det(A) = 0 if and only if the columns of A are linearly dependent.

A: Let A be a 3 * 3 matrix. We are to show that det(A) = 0 if and only if the columns of A are linearly…

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: Let B= (b₁,b₂) and C= (₁.₂) be bases for R². Find the change-of-coordinates matrix from B to C and…

A: