(1) Determine if the following questions are true or false. Assume that A and B are square matrices of the same size. = et et only if AB = BA. (a) et(A+B) Hint: Try A= (41) and and B = · ( ) (b) If the matrix exponential function e₁t is known, then one can explicitly solve d.x the intial value problem = Ax(t) where (0) = xo. dt d (c) The derivative of the matrix exponential function, (e^t) d (d) In general (eB(t)) ‡ B'(t)e³(t). Hint: Try B = dt = AeAt

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Q: dim(M23) 6. 3 O 2 O 5 None ||

A: dim(M23)Solution→    dim(M23)Now let M23=a11a12a13a21a22a23Now we can have linear combination of…

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A: A necessary condition for the inverse of a matrix that it must be a non-singular matrix.

Q: fınd the inverse of the matrix A

A: 4404110-130-3161436-1Augment with a 4x4 identity matrix=4404∣ 1000110-1∣ 010030-31∣ 001061436∣…

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Q: 6) Let I denote the 2 x 2 identity matrix. (i) Given the equation: (1+24¹) 1 12 26 T (ii) Given the…

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Q: Please don't provide handwritten solution ...

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A: and We have to solve matrix equation .

Q: Find the inverse of the following matrix. The constant a may be any real number. -5 a w G) » [* %)…

A: Given information: The 2×2 matrix is given: 0-5-1a where, a is constant. Here need to find the…