show that if A cnal B are on singu lar (AB)=B A matricesythen %3D

Q: et A be a 4x4 singular matrix. What is the smallest possible dimension of Null Space of A?

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Q: | 1 2 -1 4 | | 3 3 5 0 | | 2 1 1 3 | | 4 2 2 1 |

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Q: Let Q be an m x n matrix with columns forming an orthonormal set. Show that (Qx) · (Qy) = x · y for…

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Q: Show that ex and e−x are linearly independent in C(−∞,∞).

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Q: Determine the Linearity of this DE. * ay dy ニ X Linear O Non-Linear

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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: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: Find the inverge of the 2x2 matrix Cos t Sin t - Sine Cose

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Q: Find the singular value decomposition R= UEV• for the matriz 2 2 R=|3 4 4 5 5 6

A: We are given that R=1122344556. Now, RRT=247911481418227142532399183241501122395061. Now, finding…

Q: Explain the relationship between the statistical GM: Y, = Bo + B] x; + u;, teN and the estimated…

A: and the estimated orthogonal decomposition:

Q: Compute the product M (0)0 (7) as a 2 x 2 matrix. What kind of isometry is this product?

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Q: 4. Determine the gradient and the Hessian of the following function f(2) = a|l2| + ||Az - b|? where…

A: To find- Determine the gradient and the Hessian of the following function fx = αx2 + Ax - b2 where x…

Q: Find non singular matrices Pand Q such that PAQ is normal form 123 1. Ans. p = Q = 0 31 2 0 0 1

A: The given matrix is, A=123312 The given matrix A is of order 2×3, so pre-multiply A by I2 and post…

Q: Show that the matrix is invertible and find its inverse.

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Q: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

A: As per given  We have find solutions

Q: %3D S.

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Q: #2. Find invertible matrxes B and C SO C M.B =

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Q: How many matrices are there in the vector space Mm×n(Z2)?

A: Here, Z2 has two elements 1 and 0.

Q: Find invertible matricer A and B Cuch th at A+ B is singular. Find cingul ar matrices A and B such…

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Q: Findthe Linear Eransfromation whose matrix MT with regard to the base to mec2And the natural ruleto…

A: Given T:C2→C3 be a linear transformation whose corresponding matrix is given  MT=i-i1+i-21-1+2i and…

Q: (d) Suppose y is a least squares solution to Cx = d (for some matrix C and vector d). Show that d-Cy…

A: Introduction: Least square approximation is a method to approximate a system of equations, mostly…

Q: Now assume that f and g are both C2. Express the matrix of second derivatives V²F(x) in terms of f…

A: b)

Q: 5. Conclude from this that if b x c = 0 then b is a scalar multiple of c or vice versa (b and e are…

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Q: If Pis the projection matrix onto the line through (C) (:) and then I - P projects onto the line…

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Q: Every second order tensor can be uniquely decomposed into a symmetric and skew- symmetric part.

A: Tensor-  A tensor is a term or an object whose sole purpose is to define physical properties in…

Q: Suppose that one of the vector functions is a constant multiple of the other on the open interval I…

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Q: Го 6. Show that the matrix does not have an LU decomposition by considering the product [l11 0 [121…

A: Given :0110

Q: Let A be an x frove that mxh matrix

A: Given A be the m×n matrix. So A* be the transpose of 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: Find the standard matrix of the linear operator M : R R' that first project every vector through…

A: We have to find Standard Matrix of Linear Operator  M : R3 -> R3

Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: Suppose masses m1, m2, m3, m4 are located at positions x1, x2, x3, x4 in a line and connected by…

A: (a) The 4 x 4 matrix equation relating the column vectors f and x will be:

Q: In C[-1,1], with the standard inner product f(x)=ex and f(x)=e−x are orthogonal. true or false?

A: true please see explanation in step 2

Q: Suppose the matrix A = {a} is banded in the sense that aj = 0 %3D when |i – j| > d. Prove that the…

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Q: Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes…

A: As per the question we have to to find the transformation matrix which reflects any point on 2d…

Q: a, b eR olmak üzere, x1+ 0x2 + 0x3 = 2 %3D xi+ x2 + 0x3 = b-2 Ox1 + 2x2 + (2a – 2)x3 = b %3D %3D -xi…

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Q: Show that,in LU decomposition, the number of operations required to find U is 2 1 1 for a n x…

A: Consider the process of Gaussian elimination applied to the n×n matrix, A=a11…a1n⋮⋱⋮an1…ann be n×n…

Q: Show that I1fll= 1 forthe functional of 7be aLineur funct i'onal on X de fined by fcx)=

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Q: Theorem: For AC Cmxn, R(A)IN(A*)

A: We need to show that R(A) is perpendicular to N(A*).

Q: Consider the ARMA(3,1) model represented by y, – 0.8y,1-0.25y,-2 +0.2y,-3 = e, -1.2e,1. (a) Is it…

A: Given the ARMA(3,1) model as yt-0.8yt-1-0.25yt-2+0.2yt-3=et-1.2et-1

Q: Show that the “conic” x2 + 3y2 − 6x + 12y + 23 = 0 has no points.

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Q: Let A be a 4x4 singular matrix. What is the smallest possible dimension of Null Space of A? A) 2

A: Using,  Rank- Nullity Thereom

Q: Suppose that the deformation of a continuous body is given by 1 x(X) = (3 – 2X1 – X2)e1 + (2 +;X1 -…

A: The deformation of a continuous body is given by χX=3-2X1-X2e1+2+12X1-12X2e2+X3e3 The matrix…

Q: Transcribe the hamiltonian onto the Heisenberg square 为 B 2a

A: Given Hamiltonian  H^=α3ββ2α Trace of the matrix=Eigen values…

Q: Find the standard matrix for the stated composition of linear operators on, orthogonal projection on…

A: Reflection Matrix about the xy-plane is : Rxy=10001000-1 Reflection Matrix about the xz-plane is :…

Q: A=30 ,B = Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C)…

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Q: find the Linear transfromation TiR'+Pe) 1. whose matrix MT 2. 3. 7 1 4 Relative tothe natural baseto…

A: