Let M3(R) be the set of 3 × 3 matrices with real entries. Define the sets  V1 = {A ∈ M3(R)| A is upper triangular }, V2 = {A ∈ M3(R)| A is invertible }, V3 = {A ∈ M3(R)| a1,1 + a2,2 + a3,3 = 0}. For each of the three sets, show whether or not it (a) is closed under addition (b) is closed under real scalar multiplication

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A: (C)

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.