Question
If A, B, C, are three matrices, then AT + BT + CT is -
- zero matrix
- A + B + C
- – (A + B+ C)
- (A + B + C)T
The correct answer is: (A + B + C)T
To find the equivalence relation of
.
By the property of matrices, ![A to the power of T plus B to the power of T equals open parentheses A plus B close parentheses to the power of T](data:image/png;base64,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)
Therefore,
= ![open parentheses A plus B plus C close parentheses to the power of T](data:image/png;base64,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)
the equivalence relation of is
.
Related Questions to study
If A and B are matrices of order m × n and n × m respectively, then the order of matrix BT (AT)T is -
If A and B are matrices of order m × n and n × m respectively, then the order of matrix BT (AT)T is -
If A =
and B =
, then (AB)T is-
If A =
and B =
, then (AB)T is-
If
is square root of I2, then
and
will satisfy the relation -
If
is square root of I2, then
and
will satisfy the relation -
If A =
then A2 – 5A + 6I =
If A =
then A2 – 5A + 6I =
If A =
, B =
, C =
, then which of the following statement is true-
If A =
, B =
, C =
, then which of the following statement is true-
If A =
and B =
, then -
If A =
and B =
, then -
equals-
equals-
Statement - I For any real value of or
the value of the expression
0 or y≥2 (either less than or equal to zero or greater than or equal to two)
Statement - II for all real values of
.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason
Statement - I For any real value of or
the value of the expression
0 or y≥2 (either less than or equal to zero or greater than or equal to two)
Statement - II for all real values of
.
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason