Identify it as either an invertible matrix or not an invertible matrix for each of the following descriptions of a square matrix below. Use a theorem to justify each of your answers. (a) A 3 × 3 matrix with vectors v, u and (2v − u) as columns.  (b) The following matrix, where a is nonzero    0 a a  a 0 a  a a 0    (c) A matrix A similar to a matrix B that is orthogonal.

Q: Prove that the column vectors of the matrix B = space of the matrix B. U 2 128 0 4 2 are dependent.…

A: The given matrix .The aim is to prove that the column vectors of  are dependent and describe the…

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

A:

Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

A:

Q: 5. Describe to Mr. Dr. Prof. Meso how to input this matrix into mathway, and use mathway to reduce…

A:

Q: 100 A = 0 2 1 022

A: The matrix A3×3 can be represented as a product of LU=A where L=100l2110l31l321 and…

Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A:

Q: Let A and B be two square matrices. Assume that both A and B are invertible. Show that BA is…

A: Note that--- If determinant of a matrix is non-zero then the matrix is said to be invertible and if…

Q: Q3: Write the following matrices in the form B = U A where U is the product of elementary matrices…

A: Given matrix is  A=40-2-301210               (i) Let us consider the augmented matrix AI Now,…

Q: Find a vector that is orthogonal to each of the three vectors below: V1 = 1 V2 = 0 1 0 and V3 = 1 3…

A:

Q: Consider the following (real, symmetric) matrix: A-(10 40 = 40 158 Determine the real canonical form…

A: Given:  A=104040158 To find the real canonical form of a given matrix.

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: (g) Consider the following matrices: 0 -i 3 -V2 -V3 1 M1 i -i M2 1 2 State whether these matrices…

A: According to our guidelines we can answer three sub-parts and rest can be reposted.

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: For the following matrices, use the Invertible Matrix Theorem to geometrically describe the vectors…

A:

Q: Given the matrix 1 0 1 -1 1

A:

Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

A: We have to determine u is in Col.E, the column space of E.

Q: Determine whether the following matrix is diagonalizable or not. If yes, diagonalize it; if not,…

A:

Q: 3) Consider the following matrix: A= 020 100 0 4 1 - 1 - 1 (i) Compute A™ ¹. (ii) Write A as a…

A:

Q: Let A be a 3 × 3 matrix, and let v1, V2, V3 be non-zero vectors in R³. Suppose that Av1 = V1, Av2…

A: It is given that Av1=v1, Av2=2v2 and Av3=0

Q: Orthogonally diagonalizable the following matrix 2 1 1 C = -1 1 1 0 -1 1.

A: The solution is below.

Q: Determine whether there exists an invertible matrix A if A² = AB + 2A, where B is the following…

A:

Q: If A is a square matrix such that A = A1, then A must be equal to either the identity matrix I or…

A:

Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

Q: Let D = {(x, y) | 2 <r S 3, , -<0<0}. Sketch the region D, and evaluate the double integral lp -4y…

A: We will use polar coordinates.

Q: Consider the square matrix below: 2 -4 A = 3 2 O -2 Use Doolittle's method, expressed the given…

A:

Q: A = [2 -1 0 1; 3 5 7 -1; 1 4 2 7] List the row and column vectors of the matrix.

A: Given :                 A = 2-101; 357-1 ; 1427 To find :               List the row and column…