Prove k(A+B) = kA+ kB (matrix)
Prove k(A+B) = kA+ kB, A and B is any matrix that is suitable. Hence, k(A+B) = kA+ kB is always true.
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Prove that If det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is also an integer.
If det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is also an integer. Ans: By using the adjoint method to find the inverse of a matrix, we know that A ^ (- 1) = 1 / | A | (adj (A)) and if det (A) = 1 then, A ^ (- 1) = adj (A). The next step is to compute the adjoint matrix of cofactors and cofactor do tansposisi the matrix in which all entry (entries) in A are integers will cause cofactor searched, they also are in the form of an integer. Therefore, all proceeds in A ^ (- 1) is also an integer where A ^ (- 1) = adj (A) after adj (A) is an integer. In short, if det (A) = 1 and all entry (entries) in A is an integer, then all income in A ^ (- 1) is an integer also been proved.
det (2A) = 2 det(A) is it true?
det (2A) = 2 det(A) Prove it is true or false. So from above we can see tat the statement is false. However ....... matrix 1x1, [9] Although the general equation is false, but in matrix 1x1 with specific example have proven that the statement is true. So we can conclude that the statement is sometime false.