Question 1. Let A be an m × n matrix with real entries. Let T₁: R → Rm be the corresponding linear map, and let DTÂ be its matrix derivative. Show that DTA = A.

True or false? det(A) is defined only for a square matrix A.

Let A be a 8×7 matrix. What must a and b be if we define the linear transformation by T: R^a → R^b as T(x)=Ax?

Explain how to determine whether a function T : V → W is a linear transformation. Secondly give some example along with proper explanation where this T can be treated as matrix.

Need help with this question. Please explain each step and neatly type up. Thank you :)

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