Let T: R²→R², [2] → [ Show that T is invertible, and find a formula for T-¹. -5x1 +9x2 4x1 - 7x₂

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I need some help with a linear algebra problem involving traffic flow networks.  The goal is to find the flow rates (f1 through f5) and analyze an augmented matrix. When I did this, I got confused in finding the flow rates... my answer doesn't resemble the vector format it should look like (shown in the last figure). Could I get some assistance to better understand how to set up this problem and find the flow rates? Thank you.

Subjects;

It is true or false that every 6×6 matrix has an inverse.

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Step 1. Dimension Analysis Observe that the two given matrices are the same size. Namelų, the matrices A and B each have dimensions: Consequently, their products AB and BA also each have the same size. Namely, the products AB and BA each have the dimensions: Step 2. Calculate the matrix product AB and enter your results into the table below. Simplifų your result as much as possible. If the answer is undefined, leave the answer blank.or type the letter:N В АВ -4 1 12 12 -13 6. -14 8. 0. 3 7. - 1

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Explain the following terms by use of examples: Special matrices Associative law in matrix algebra input output analysis