4. If A is 4x4 normally distributed random matrix and I is 4x4 identity matrix. Proof that: a) A'A = I b) A is not a singular matrix (use two different solutions). c) A-1| |A| = 0 d) A"A = AA

Q: 8. so that detA =25, trace-10, and à-5 is repeated. Q24. Complete the matrix A = [8 - 3] SO a) 3 2…

A: Sorry to say that, According to our guideline we can answer only first question other can be…

Q: -1 0. 3. 17. Let A = 3. B = 4. Compute the 2. 10 2. 2 5 following matrix products (if possible). (а)…

A: To find  (a) AB, and  (c) BC, we use the definition of the matrix multiplication. The multiplication…

Q: 3. Let A be an n x n singular matrix. Describe one way to construct a non-zero matrix B such that AB…

A:

Q: 17- Let A be 5 x 5 matrix and det(4) = 2. What is the value of der(24)? a) 128 b) 32 16 64 LEave…

A:

Q: Let A be an n x m matrix. What is the value of rank(A) + nullity(A)? A) т B) n +1 C) m + n D) т — п…

A: given matrix A is of order n*m to find  rank(A) + nullity(A)

Q: 4. Let A be a square matrix with transpose A". • If AT = A, then A is called a symmetric matrix. %3D…

A: If A is non singular then A is non zero. ATT = A

Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

Q: Suppose A is a matrix such that A² + A = I, I is the identity matrix. Show that a) A must be square.…

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Q: a) If A is a square matrix satisfying A2 = 0, then A = 0. b) If A is a sqaure matrix satisfying…

A: (a) FALSE    (b) FALSE    (c) TRUE

Q: 5) Le Let A be a 6x5 matrix with. hullity of A? a rank of 2. what is the

A:

Q: and Let A be a 2 x 2 matrix which satisfies Av₁ = 2v₁ and Av₂ = ₂ where ₁ [B] - [1] = [] compute 1th…

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Q: 2. Let A be the matrix shown below A = [22] :) Find the matrix P that diagonalizes A.

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Q: es m- Exercise 2.3.34 If A and B are n x n matrices, show that: a. AB = BA if and only if (A+B)² =…

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Q: 10) Let A E Mnxn be given by 0 0 ao ... -1 .. A = -1 0 a2 .. 0 0 0 • -1 an-1 .. Compute XA(t).

A: