If Q-I- auu" where Qis an orthogonal matrix, a> 0, and u E Rx1 real vector, and I is nx n identity matrix then 6au-1 O b. lu|- 2 O d. lu|| - 0.5

Q: If (AB)" = and A = find the matrix B. %3D

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Q: Please give me an example of Mathematical formulas of a 3 x 3 matrix of Hermitian matrix. Make sure…

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Q: What is the relationship between a matrix and the i-hat and j-hat vectors

A: matrix is used to find the cross product of two vectors detailed solution is given below

Q: 8) Show that the matrix -1 Bz 1-4 4 -3 -2 is idempotent.

A: Given…

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

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Q: Answer considering the matrix with the given vectors as its columns

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Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

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Q: If A * I = A, and A is a 3x5 matrix, what are the dimensions of I? Show complete solution as proof.

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Q: What is the matrix representing a translation by vector [−1, 2, −1]? What is the matrix representing…

A: The given matrix is -12-1. The rotation angle at 90°. So if the rotation is θ around Y axis is,…

Q: A vector is rotated about the Y-axis 45 degrees and is subsequently rotated about the fixed X-axis…

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Q: 4. Prove: If b is a non-zero vector, and x and x are both solutions to the matrix equation AX =6,…

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Q: Find the coordinate matrix of x = (1, 2, −1) in R3 relative to the (nonstandard) basisB′ = {u1, u2,…

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Q: Explain  column vector of m x 1 matrix?

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Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Given :                To find the distance of a point in the 3-D system from the origin

Q: 2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0…

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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: = (3, 6) 2. It is known that u = (-2,3) and v = relative to the inner product in R? which is derived…

A: 2 Given that u=−2,3 and v=3,6 And A=2134. We have to find the u and v. We know that…

Q: 2. Write the matrix that could be used to rotate a vector 200 degrees clockwise about the origin.…

A: We have to find the matrix that could be used to rotate a vector 200 degrees clockwise about the…

Q: a() – 4 (6) - (1) - (-) - Find a 2 x 2 matrix A such that A

A: We have to find a 2 × 2 matrix A such that A12=A23=41 Let the matrix A = abcd

Q: How do I find a basis for {(2c, c, b)} | b, c ∈ R}? I tried writing it as a linear combination and I…

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Q: g.... r, be vectors in R", and let Q be an mxn matrix. Write the matrix Qr, Qr, as a product of two…

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Q: Let A be an m x n matrix with rank m and B be ann x p matrix with rank n. Determine the rank of AB.…

A: to find the rank of AB.

Q: (a) Find the matrix A so that AB=C, where а, а, а, B= b, b, b, & C= b, b, b, a, az az (2 rows are…

A: Given B=a1a2a3b1b2b3c1c2c3 now using row operation R1↔R3 ~c1c2c3b1b2b3a1a2a3

Q: Number 7 Construct a 2 x 2 matrix A such that the solution set of the equation Ax= 0 is the line in…

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Q: 3) Find the vector projection of A onto B. (Projs A). b\ If possible, use matrix inversion method to…

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Q: (3) If A is a real 2 by 2 matrix, A-(::) a b and a is a two-dimensional column vector, what…

A: Please check step 2 for the solution.!

Q: a The fallowing A ond B!, matrices goveric 3* madrices are How wouldyou OL express, the Sum a the…

A: Given matrix is, A=a11a12a13a21a22a23a31a32a33B=b11b12b13b21b22b23b31b32b33

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: Construct 4x4 matrix A= Lajj whose a entries satisfy Ja;;=2i ij=1, 2, 3,4 %3D

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Q: Let y = and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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Q: L- matrix and U

A: The objective of the question is determine the L- and U- matrix.

Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

Q: 4 Compute x using the vectors w = -2 and x = (Simplify your answer. Type an integer or simplified…

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Q: 5. Let x and y be vectors in R" and let Q be an n x n orthogonal matrix. Show that if z = Qx and w =…

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Q: 1 %Create a matrix A whose elements are the same as matrix but the fourth column is the column…

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Q: Show that for itermitian matrix C any S hew that

A: To prove: ρ(C) = C2

Q: Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R'…

A: System of linear equations

Q: 4. and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.…

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Q: find the given matrix is Identity matrix if not find determinant of the matrix without ing NumPy…

A: For Identity matrix, the diagonal element of the matrix should be 1 so its determinant always 1 and…

Q: Find the coordinate matrix of x = (-17, 22) in R² relative to basis B' = {(-5,6), (3, –2)}. %3D %3D

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Q: 7. Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u. Let y =…

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Q: 2 2 1 2 -1 2 is orthogonal. Verify whether the matrix A = 3. -1 2 2

A: Given matrix is, A=132212-12-122

Q: If you keep the same basis vectors but put them in a different order, the change of basis matrix B…

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Q: Let y = and u= 3 Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to…

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Q: 2(b) Th picopert matrix not to Prove matria does r

A: A matrix is defined as a rectangular array of numbers or objects. The arrangement takes place into a…

Q: Let y= and u= Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u.…

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Q: 9 0 3+i 7 4 2- i A= 2+ i 9 3- i

A: Let  A=42-i92+i03+i93-i7 To find the null space we need to find a vector X=xyz, such that AX=0, we…

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.