.1 Show that the set M of all m × n matrices with their elements as real numbers is a vector space over the field F of real numbers with respect to addition of matrices as addition of vectors and multiplication of a matrix by a scalar as scalar multiplication.
Q.2 The temperature ‘u’ is maintained at 00 c along the three edges of a square plate of Length 100 cm and fourth edge is maintained at a constant temperature ‘u0’ until Steady state conditions prevails. Find an expression for the temperature ‘u’ at any Point (x,y) . Calculate the temperature at the center of the plate.
Q.3 Solve x(y^2 + z^2) p + y (z^2 + x^2) q = 2 (y^2 – x^2)?
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