Find a 2 x 1 matrix x with entries not all zero such that 2 Ax = 3x, where A = 1 2

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: Find the 2, 3-cofactor of the matrix 1 2 0 0 2 1 -1 7 -3 0 0 0 7 1 0

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Q: Find a 2 x 2 matrix such that 3 -2 -2 = 61

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Q: X1 + 3x2 – 2x3 + 2xs = 0 2x, + 6x2 – 5x3 – 2xg+4x5 – 3x6 = -1 X3 + 5x4 + 3x, = 1 x + 3x2 + 4x4 + 2xs…

A: Given that the system of linear equations is…

Q: Compute the adjugate of the following matrix: -7 3 -6 0 0 0 0 0 0 0 0 0 adj -7 0 -2 %3D | 2 -8 4

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Q: Given A = 1 0 0 -3 1 1 1 - 2 -1 " x = and b = 300 150 400

A: Given that the system Ax=bHere A=1-3101-201-1 , b=300150400

Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

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Q: Is the following matrix diagonalizable¹? 3 B=0 0 -3 1] 3 1 0 3

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Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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Q: Express the quadratic equation in the matrix form x Ax + Kx + f = 0, where a Ax is the associated…

A: The given quadratic expression is .We need to convert this quadratic in the form .

Q: If A is a positive definite matrix and B is positive semi-definite, show that trace (AB) 2 O with…

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Q: Find the matrix B such that 2AT+3B=0.

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Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: 2. Diagonalize the matrix: 1 0 -2 1 1 1 -1

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Q: Let y= Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u. and u=…

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Q: 1 1 4 1 2] 01 21 1 0012 -1 0 0 2 1601 D) Find the rank of the matrix 0 1 2

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