If A and B are similar, then there exists a matrix P such that Bk = P-1AKP. Use this fact to find B“, where B = p-'AP, for the matrices %3D 2 0 A = B = p-1 0 1 -1 * =

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

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

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Q: Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation [1 0 0 1 АВ - ВА. %3D

A: In this question we have to prove that no 2×2 no matrices the given matrix equation.

Q: Suppose that 60% of the people who own a GM car buy a GM car for their next vehicle. Also, suppose…

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Q: If a 6 x 3 matrix A has rank 3, find dim Nul A, dim Row A, and rank AT .

A: We are given that a 6x3 matrix A has rank 3. So, dim(Row A) = 3. We know that dim(A) = dim(Row A) +…

Q: f A is 3×3 nonsingular matrix such that AAT=ATA and B=A-1AT then BBT=

A: Given that: A is 3x3 non singular matrix and AAT=ATA and B=A-1AT

Q: Which of the following matrices is not in Row Echelon Form (REF)?

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Q: If A and C arę nxn invertible matrices and B is an nxn matrix, then

A: By Theorem we can say that

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Suppose AB = I, . Show that the equation Bx=0 has only trivial solution. Explain why the matrix not…

A: Suppose that AB=In (then x n  identity matrix). The objective is to show that, the equation Bx=0…

Q: -14] is a linear combination of the vectors 16 if and only if the matrix equation Az = b has a…

A: Solving

Q: Find a 2x2 matrix that forms an angle of n/3 cadians with the matrix P -- (: 9) 2 0 0 2

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Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: A and B are 3,3 matrices. Lo lAl =-3 and IBl =2. SO phat is l-2A02|?

A: Properties of determinant:kA=knAAB=ABA-1=1A

Q: Find 6×6 matrix a, that satisfies the stated condition. Make your answers as general as possible by…

A: Let the genral 6*6 matrix is given by…

Q: Suppose that Q is 3 x 2 matrix with orthonormal columns then Oa Q'Q +1 Ob QQ" - I OcQ" - Q Od. Q"Q-…

A: The detailed solution along with the final answer is described below.

Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: Suppose a 5x4 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Multiple :    Let  A be 5 × 4 matrix . We have given that , rankA = 3. We need to find , dimension…

Q: 2) If IAI = 3, where A is a 3x3 matrix, caleulate the folowing: 2a) det ( ZA) 26) det (A) 2c) det (…

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Q: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: Show that any matrix of size 3 by 3, can be written as the sum of two invertible matrices, that is,…

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Q: Show that if a 3×3 matrix A is never sad then the entries along its diagonal, i.e. a11, a22, a33,…

A: Let 3×3 matrix A is never sad

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: Suppose column 4 of a 3 by 4 matrix is all zeros, then x, is certainly a free variable. The special…

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Q: (4) Let A be a 3x3 matrix. If |4|= 2 , then |3.4|=,

A: Given that A be a 3*3 matrix and |A|=2. To find the value of |3A|

Q: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

Q: Find the column space of the 10 × 20 matrix A if the system Ax = b is solvable for every b. Justify…

A: Note that : Ax = b has a solution if b lie in column space of A.

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

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Q: Let A be 5x1 matrix. Knowing that Rank (A) = 2. Then Nullity(A) is equal to: O 2 ONone of these

A: The solution is given below in the next step:

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: If A and B are orthogonal nxn matrices, then AB-1 is an orthogonal matrix. True False

A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

Q: 2) Find the rank of the matrix A = 2 3 -1 ー1 1- ー2 -4 3. 3 -2 3. By deducing imto Echelon form.

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

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: Suppose that A is a 16 x 14 matrix that has 6 pivot columns. Then: (i) dim (ColA) is (ii) dim(ColA)-…

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Q: Find 6x6 matrix | a, that satisfies the stated condition. Make your answers as general as possible…

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Q: If the rows of an mxn matrix A are linearly independent and Ax=b is consistent then it has unique…

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Q: Suppose A = UDVT where U and V are n x n matrices with the property that UTU = I and %3D vTV = I,…

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Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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Q: Find SVD for the matrix A=[1 2;2 1].

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Q: what is the Dim of a matrix, like if there is Matrix A, what is Dim(A)? Can i have example too?

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Q: 29 What numbera in A-L makes A-QA@ possible (where Qis an orthognael matrix and A is an Zero or 1??

A: We shall solve this question by just using the definition of an orthogonal matrix. We know that a…

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

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Q: If A is a skew-symmetric matrix then show that AAT = AT A and A² is symmetric. [Note AT denotes the…

A: We will use definition

Q: Find a 3 x 3 orthogonal matrix P whose first two rows are multiples of (а) (1,2,3) and (0, -2,3),…

A: To find the matrix

Q: solve for matrix Colfficients A. CCX=l,y=l-),2=0]] 3.CCx=1,y=1,2 =]] CCa--4),-(-1をこ0 CCX=3,y=3,=)…

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Q: The coordinates of the end of a line is at P (0, 0, 1) and at Q (1, 1, 1). Represent mathematically…

A: Given that the coordinates of the end of a line is at P (0, 0, 1) and at Q (1, 1, 1). So the…

Q: Let A be a 5 × 4 matrix. Can the equation Ax=b be consistent for all b in ℝ5 ? Explain, please. Can…

A: Given that, A is a 5×4 matrix. Consider the equation, Ax=b. Here x is a 4×1 matrix with n=4 unknowns…