What conditions must a, b, c and d satisfy for the matrices: 3 a [22] [] and [1] -2. b d to be linearly dependent?

Q: if A and B are matrices and K is a scalar

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Q: 1. Let, A = -1 21 Find the matrix -5A3 + 2A? + 4A + 512. 9 21

A: Given: A=-1292 Determine A3. A3=-1292-1292-1292=192922-1292=-14218962

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

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Q: Let A =  -2 1     0 3     and    B =  2 -3     1 −2. Find a matrix X satisfying the matrix…

A: The given matrices, A=-2103 and B=2-31-2 We have to find the matrix X, that satisfies 2A+X=3B

Q: 4x+5y+4z = 8 3x+3y+ z =-9 5x+5y+2z = -1 Write the augmented matrix:

A: For a system of equations is a matrix of numbers in which each row represents the constants from one…

Q: B = %3D 0 -4 2 -8 1 2 -3 7 3 -1 -2 -8 -1 20. Can every vector in R* be written as a linear…

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Q: compute the indicated matrices A + 2D

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Q: 2. For matrices To and 3 show that A³+ B = I, -20 B= 8 where I is the 2 x 2 identity matrix.(4…

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Q: 1 2 -4 -8 (b) -2 -4, 8 16 This set is

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Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Find The general solution 2 K (34 cosx + 4x +ex²³ )dx=2 sinx+ Daly O

A: The given ODE is of the form M dx + N dy = 0  where M=3y cos x + 4xex + 2x2ex and N=3sin x+3.…

Q: Let 1 1 -2 1 2 3 | A = 1 4 and B = -6 -2 -3 - -3 2 1 -1 -1 | Find the inverse of the matrix A + B –…

A: Let's find.

Q: Show that the equation of the line through points (a1, b1) and (a2, b2)can be expressed as the…

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Q: Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A*…

A: Please check step 2 for the solution.!

Q: compute the indicated matrices D +BC

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Q: Q8: Given that -2 X = 1 8 -8 -9 -9,Z -7 7 -2. -8 5 what is the matrix 3X + Y – 3Z?

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Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

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Q: a) Consider the matrices A and B: 4 -3 A =-2 7 1 8 6. -5 B = -3 -2 Which element is in row 2, column…

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Q: Find a non-zero 2 x 2 matrix such that Note: 4890 -7 -67 28 24 =

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Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: 3. Let A=1 -1 4 -3 7 and B= 6 -24 -6 18 Find the matrix X that satisfies the matrix equation…

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Q: Determine the rank of matrix A, where: A = 1 0 -1 39 0 0

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Q: If %3D 1- C What me matrix of An11n5 a positive inverse integers).

A: If we know how to inverse a matrix process we can solve the above question

Q: compute the indicated matrices A3

A: Here given

Q: Q2: Find the inverse of the matrix M =

A: The given matrix is: M=-312-1 Formula: The inverse of the matrix A=abcd is: A-1=1ad-bcd-b-ca By the…

Q: 1. Write the following linear system in matrix form. 2x, + 3x₂ <= 0 3x₂ + x₂ = 0 2x,

A: NOTE: As per our guidelines, I have solved one question (Question number 1) out of many. If you want…