Find u and usuch that the null space for the matrix U= 3 v= 0 -2 1 1 -3 -15 1 - 9 1 is span{u, }.

Q: Construct a matrix whose column space contains (1, 1, 1) and whose nullspace is the line of…

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Q: Find the nullspace of the matrix

A: By definition , nullspace of a matrix A is the collection of all vectors x such that Ax=0 Given…

Q: Show that the zero matrix is the only 3 × 3 matrix whose null space has dimension 3.

A: Given- A zero matrix of 3×3 order. To show- that the zero matrix is the only 3 × 3 matrix whose null…

Q: > LS A-8 null matrix ?

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Q: Find an invertible matrix U such that UA R is the [21 1 -1 -1 0] -12 1 1 A = 3 -1 1-2 3

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Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: Construct a 3 by 3 matrix whose column space contains ( 1, 1, 0) and ( 1, 0, 1) but not (1, 1, 1).…

A: Column space: The set of columns of a matrix which are linearly independent is called the column…

Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: Find ∣A−1∣ for the matrix

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Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

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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: The symmetric matrix corresponding to the quadratic form X1 x2 = x} – 2x1x2 + 2x1x3 – 3x + 4x2x3 –…

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Q: find if the vector x is in the range for matrix A

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Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: stable

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Q: Let A = (2 1, 2 3) . Find a 2 x2 matrix X so that X^2 = A

A: Matrix A =[2 1, 2 3]  We have to find 2*2 matrix X such that X2=A

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: the acdjainbaf square of As of 2.

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Q: 3= b, ,b2} and C= (c,.c2} be bases for a vector space V, and suppose b, = - 6c, + 5c2 and b2 = - 4c,…

A: Two bases B and C of a vector space V are given. We need to find change of co-ordinate Matrix from B…

Q: 2. Find a matrix that projects onto the line / 2x - 5y = 0 and find the projection of 6= (1, -2)…

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Q: If the matrices A and B are conformable for sum A+B the product AB then prove that (A+B)" = A" +B"…

A: Prove that. (a).A+BT=AT+BT(b).ABT=BTAT