Determine if the statement is true or false, and justify your answer. If C_1 is

Question

Determine if the statement is true or false, and justify your answer. If C_1 is the change of basis matrix from B_1 to B_2 and C_2 is the change of basis matrix from B_2 to B_3, then C_1C_2 is the change of basis matrix from B_1 to B_3. True. We have xB_2 = C_1xB_1 and xB_3 = C_2xB_2 So C_1C_2 is the change of basis matrix from B_1 to B_3. True. We have xB_1 = C_1xB_2 and xB_2 = C_2xB_3 So C_1C_2 is the change of basis matrix from B_1 to B_3. False. We have XB_2 = C1xB_1 and xB_3 = C_2xB_2 So C_2C_1 is the change of basis matrix from B_1 to B_3, not C_1C_2. False. We have xB_1 = C1xB_2 and xB_2 = C_2xB_3 So C_2C_1 is the change of basis matrix from B_1 to B_3, not C_1C_2.

Explanation / Answer

Option c is correct.You have followed the right procedure which is mebtioned in the option.since xb3=c2xb2=c2c1 xb1.

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