Consider a 2 × 2 matrix $M = \left[ {\begin{array}{*{20}{c}}{{v_1}}&{{v_2}}\end{array}} \right]$, where, v1 and v2 are the column vectors. Suppose ${M^{ - 1}} = \left[ {\begin{array}{*{20}{c}}{u_1^T}\{u_2^T}\end{array}} \right]$, where uT1 and uT2 are the row vectors. Consider the following statements.Statement: uT1v1 = 1 and uT2v2 = 1Statement: uT1v2 = 0 and uT2v1 = 0Which of the following options is correct?

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TuteeHUB · Accepted Answer

Both the statements are false

TuteeHUB · Answer

Statement 1 is true and statement 2 is false

TuteeHUB · Answer

Statement 2 is true and statement 1 is false

TuteeHUB · Answer

Both the statements are true

1.	Consider a 2 × 2 matrix \(M = \left[ {\begin{array}{{20}{c}}{{v_1}}&{{v_2}}\end{array}} \right]\), where, v1 and v2 are the column vectors. Suppose \({M^{ - 1}} = \left[ {\begin{array}{{20}{c}}{u_1^T}\\{u_2^T}\end{array}} \right]\), where uT1 and uT2 are the row vectors. Consider the following statements.Statement: uT1v1 = 1 and uT2v2 = 1Statement: uT1v2 = 0 and uT2v1 = 0Which of the following options is correct?
A.	Statement 1 is true and statement 2 is false
B.	Statement 2 is true and statement 1 is false
C.	Both the statements are true
D.	Both the statements are false
Answer» D. Both the statements are false

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