Question 1. Let A be a 2 x 2 matrix with linearly independent column vectors a₁ and If a₁ a2. and a2 are used to form a parallelogram P with altitude h (see the figure), show that h²||a₂||² = ||a₁||² ||a₂||² — (afa2)² a1 $ a2 α a2 a₁

Q: T 1 0 +2 0 2 3. Find the matrix A if : 3 1

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: If A and B are similar, then there exists a matrix P such that B = PAP. Use this fact to fi -2 2 -3…

A: Here we have to find B5 ,   We have to find if A and B are similar or not, if A and B are similar…

Q: Įsin x cos^(3/2) x dx * O -2/5 cos^(5/2) x + C O None of the choices -5/2 cos^(5/2) x + C O -2…

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Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

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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: Part I: Mark each statement True or False. If true, write “T" into the bracket; Otherwise, write “F"…

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Q: Let A be a n x n real matrix. If the rank A =n find the following: (a) Col A (b) Nul A (c) nullity A

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Q: .

A: A=02-123-2-1-20 To find: An orthogonal matrix U that diagonalizes .

Q: Find a 3 x 3 matrix A such that 1 -5 A 3 A 1 -3 and -2 A 4 1 -5 A = 3. ||

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Q: Let A be an m × n matrix. Under what circumstances will ||A||2 = ||A||F?

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Q: If Ax = ax for nxn matrix A, nx1 matrix x, and a E R, determine a scalar 3 with the property that…

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Q: Suppose that A&B are n x n matrices and A² B = I, then O a. A-1 = BA %3D O b. A-1 = AB %3D OCA-1 = A…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a…

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Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: PP, i = 1,2. Let P Let Po, P1, and P2 be points in R². We denote r; = be the (2 × 2)-matrix with the…

A: This question is about application of linear algebra

Q: Find matrices P, D and P-1 that diagonalize matrix A, where A = P = D= P-1 20 0 -11 -2 -3 -30 -1

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Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: 3 Construct a 3 x 3 nonzero matrix A such that the vector 2 is a solution of Ax = 0. A = [(1,2,3),…

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Q: For each of the following sequences, if the divergence test applies, either state that lim an does…

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Q: refer  to  image  below  which  both  address  same  question.

A: Step 1: Step 2: Step 3: Step 4:

Q: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

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Q: Let A E Rx and B E Rmxm and assume that dim N(A) = k and dim N(B) = l. Let C be an 2 x 2 block…

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Q: Consider square matrices A & B where A#0, B÷0,AB=0. Show that |A|=0 or |B|=0. 6.

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Q: 19. For the matrix A = 4) 6 -6 -4 find a general formula for A".

A: The matrixThe characteristic equation|A−λI|=0λ2−(6−4)λ+(−24+24)=0λ2−2λ=0λ(λ−2)=0The Eigenvaluesλ=0,2

Q: || 02 [1.]] -a 3 4 a +a

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

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Q: Find the matrix X, such that XDC - 2XC — ХС? + С satisfies. 3 4 4 6 6 5 C = 1 2 1 D = 1 3 -2 4 -2 -4…

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Q: Let A = B = lo ĭ [1 2 [1 0 and V = |1|. What is the sum of the entries of the C = 14 matrix V" (A" –…

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Q: Find the coordinate matrix of w= 2-3x+x?+x vector relative to base B= {1, 1-x, (1-x)?, (1-x)³} in…

A: Given, w = 2 - 3x + x² + x³