- For each of the following, decide if the statement is always true or always false or sometimes true, sometimes false w

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For Each Of The Following Decide If The Statement Is Always True Or Always False Or Sometimes True Sometimes False W 1 (161.77 KiB) Viewed 36 times

- For each of the following, decide if the statement is always true or always false or sometimes true, sometimes false when the given condition is true. (a) Given: The vectors v1, 02, V3, 04, VS, v6 span R6. Statement: The vectors 01, 02, 03, VA, VS, vo are linearly independent. always true always falso sometimes true, sometimes false (b) Given: B is a 6 x 6 matrix with det(B) +0. Statement: The equation BX = b has infinitely many solutions. always true always false sometimes true, sometimes false (c) Given: B is a 6 x 6 matrix, 6 is in R, BX = 0 has infinitely many solutions. Statement: The equation BX = b has infinitely many solutions. always true always false sometimes true, sometimes false (a) Given: B is a 6 x 6 matrix and the columns of B are linearly independent. Statement: The equation BX = b has exactly one solution. always true always false sometimes true, sometimes false (e) Given: E is a 6 x 8 matrix, b is in Rø, N(E), the nullspace of E is 2-dimensional. Statement: The equation EX = b has infinitely many solutions. always true always false sometimes true, sometimes false (f) Given: D is a 7 x 5 matrix, b is in R7, N(D), the nullspace of D is 1-dimensional. Statement: The equation DX = b has infinitely many solutions. always true always false sometimes true, sometimes false