For the matrix A, find an orthogonal matrix P such that P-¹APis diagonal. 1 1 0 1 10 [002] A = 01 01 1 100 /2 6 √2 0 0 √20 /2 1 ΤΟ 1 - 1 0 −1 −1 0 1 1 10 0 0 1 0 1 1 √20 0

Q: Find the coordinate matrix of w relative to the orthonormal basis B in Rn. w = (3, −5, 11), B = {(1,…

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Q: 3| |1 Let A 3 1 4 3 1 3 41 1) Verify that: AadjA = det(A) I (Where I is the identity matrix) 2) Find…

A: given matrix isA=1331431341) to verifyA.adj(A)=det(A).I2) to find A-1

Q: Let H be an r-by-r square matrix. Prove that (HT)−¹ : (H−¹)T =

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Q: aj bị c1 adjA if A = |a2 b2 c2| is a non-singular matrix prove that A: detA аз b3 C3

A: Matrix A is a non-singular matrix. This means; det A ≠ 0    A =a1b1c1a2b2c2a3b3c3adj A…

Q: 1 2 2 Given that matrix A = 2 1 2 2 2 1 i. Show that A? – 4A – 51 = 0 where I is an identity matrix.…

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Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(−5, 6), (3, −2)}, x = (−17,…

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Q: Find matrices A and B in M2(Z) such that AB= 0, but BA+0. 3.

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Q: Find the change of basis matrix [] and use it to find [v]• B -17] 2 0 --{@@@}-E -2 4 4 B 1 2 = -71…

A: Given Information: and To find: and Notation used: denotes the change of standard basis matrix with…

Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: Use the following matrices to perform the operation, if possible. (If not possible, enter IMPOSSIBLE…

A: C=9101D=2653

Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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Q: Use the matrix P to determine if the matrices A and A' are similar. P =   −1 −1   1 2,   A =   14…

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Q: Let X be the 3 x 3 matrix such that left-multiplication by X has the same effect as applying the…

A: In this question we have to find the (1, 2) entry of x.

Q: Let A be an Xn matrix satisfying A-34 +I= 0 where 0 is the nXn zero matrix. Then A = A² - 31, A= =…

A: The objective is to choose the correct option for inverse.

Q: For the matrix A, find an orthogonal matrix P such that P-1 A Pis diagonal. 3-2 41 A = I ده است مراد…

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Q: [a b] [add] c A² − (a + d)A + (ad – bc)I = 0 Show that the matrix A = satisfies the equation

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Q: Find the coordinate matrix of x in Rn relative to the standard basis.x = (−6, 12, −4, 9, −8)

A: The given vector is x =  (−6, 12, −4, 9, −8).One has to find the coordinate matrix of x relative to…

Q: Find a basis for the null space of the matrix. [10-7-2] A = 01 7-2 00 0 0

A: The given matrix is A=10-7-2017-20000. We have to find the basis for the null space of the matrix.

Q: ✓2.19 Find the Jordan form and a Jordan basis for each matrix. 4 0 0 (b) 2 13 5 04 (a) -10 4 -25 10…

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Q: Find the change of basis matrix [] and use it to find [v].Ⓡ. B B 0 {Q[C])} 4 [V] B 0.5 -0.5 1.5 1 16…

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Q: Give an example of a non-zero 2 × 2 matrix R which satisfics R² = 0. Suppose that M is an n x n…

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Q: 10. B =

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Q: Find an orthogonal basis for the column space of the matrix to the right. -1 5 1 -7 1 - 1 1 -3 5 2 5…

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Q: Let V1, V2, V3 be the vectors in R³ defined by V₁ = (c) Type the dimension of span{V₁, V2, V3}: -101…

A: Here,       v1 = (-10, 12, 12)t        v2 = (-37, 36, 17)t      v3 = (-7, 0, -19)t    (a) We see,…

Q: Calculate the determinant and inverse of the matrices by scaling

A: For matrix A Determinant of A = |A| = 0 As row1+ row2 = row5. Hence |A| = 0 So, inverse of A doesn't…

Q: Find vectors x and y with ||x, = 1 and ym 1 such that ||A||₁||Ax|, and A||- ||Aym' where A is the…

A: Given, The matrix  A=4-1-230-3102 We have to find the vectors x and y with xs = 1  and ym = 1 such…

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

A: The solution is below.

Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: Find the change of basis matrix from B₁ to B₂. B₁ = OLD 0 -8 eBook 4 B₂ = 2 -3 -1 3 7 4 (HH) -2 2 -8

A: The given bases  B1 and  B2  are ,   B1 =  542 ,    8   0-8  , -3   3   2    and             B2 =…

Q: (c) Consider the following matrix. [3+31 Let B = A-¹. Find b₁2 (i.e., find the entry in row 1,…

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Q: A = 700 0 30 0 000 0

A: Given matrix is a matrix of order 3×4.