D M 2P] 3 3. If A =| K [-P R s is a singular matrix then find the value of P.

Q: A B Let m and n be whole numbers. Matrix P is of order/size m x n. Matrix Q is of order/size n x m.…

A: Given that, m and n are whole numbers. Matrix P is of order m×n and  matrix Q is of order n×m. Want:…

Q: For what values of r and s is the following matrix regular?

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Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Perform the elementary row operation - R₁ → R₁ to matrix D to obtain matrix E. -1 0 0 01 2 -2 -2 1…

A: Given a matrix A=1-10002-21240101000215 To perform the row operation -13R4→R4 to obtain a matrix E

Q: Find a, b, and c for the following matrix relation to be true. 0 01 1 3 21 1 4 -1 4 OJ = la² a+b 3b…

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Q: Let A be a m x 3 matrix with columns V₁, V2, V3. Find A0, A (-0. and A 0

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Q: Let A be a real 2 x 2 matrix satisfying A? - 4A = 0, where O is the zero matrix. SKIP Find the…

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Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: For the vector field F = (z, x, y), calculate the total flux through the box [0, 6] x [0, 4] × [0,…

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Q: 3. Find x such that the matrix A is equal to its own inverse. 2 -3 A %3D 3

A: Given :  The given matrix is   A = -2-33x To find : We have to find x such that the matrix A is…

Q: A matrix A € Rmxn can also be viewed as a vector, by stacking all its n columns into a single…

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

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Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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Q: 3. Find all real numbers x, y such that the columns of the following matrix are linearly de-…

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Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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Q: Let A be a 3 x 3 matrix such that det(A) = 2. Evaluate det(Aª) and det(2A).

A: Recall the following. If A is a n×n matrix and m be any positive scalardet k A=kndet Adet Am=det Am

Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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Q: of |4|. örthogonal matrix Q. B C Q6. If A = D where B,C,D,E are n by n matrices, find |4 when BD =…

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Q: Let B = {b1, b2} and C {C1, C2} be R2. Produce the change-of-coordinate matrix from B to C and from…

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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: Determine whether A is similar B .If A ∽B, give an invertible matrix P such that P-1 AP = B.

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Q: 0 Find a non-zero 2 × 2 matrix A such that A? 0 0 A =

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Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

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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: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

Q: Prove that An nxn matrix A is non singular if and only if it can be written as a product of…

A: We prove that an nxn matrix A is non singular if and only if it can be written as a product of…

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Suppose A is an n x n matrix with A² = A. Show (I – 2A)−¹ = I — 2A.

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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: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

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: A is a reversible matrix of nXn. Show that |adjA|=|A|r1

A: As we know that the inverse of a matrix A is : A-1=adj(A)|A|

Q: Let M = -3 Find c and c2 such that M² +cqM+c»I½ =0, where I, is the identity 2 × 2 matrix and 0 is…

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Q: Let A be an m x n matrix. If the equation AX = b is consistent for some b, then Col( A) is all of…

A: Given AX= b