How to multiply a matrix by a scalar
Help Questions
ACT Math › How to multiply a matrix by a scalar
Define matrix , and let
be the 3x3 identity matrix.
If , evaluate
.
The correct answer is not given among the other responses.
Explanation
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the second element in the second row, which is 6; similarly,
. The equation becomes
Simplify the following
Explanation
When multplying any matrix by a scalar quantity (3 in our case), we simply multiply each term in the matrix by the scalar.
Therefore, every number simply gets multiplied by 3, giving us our answer.
Define matrix , and let
be the 3x3 identity matrix.
If , then evaluate
.
Explanation
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the first element in the third row of
, which is 3; similarly,
. Therefore,
Explanation
When multiplying a constant to a matrix, multiply each entry in the matrix by the constant.
Define matrix .
If , evaluate
.
The correct answer is not among the other responses.
Explanation
If , then
.
Scalar multplication of a matrix is done elementwise, so
is the first element in the second row of
, which is 5, so
Define matrix , and let
be the 3x3 identity matrix.
If , evaluate
.
The correct answer is not given among the other responses.
Explanation
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the first element in the second row, which is 5; similarly,
. The equation becomes
Define matrix .
If , evaluate
.
The correct answer is not among the other responses.
Explanation
Scalar multplication of a matrix is done elementwise, so
is the third element in the second row of
, which is 1, so
Define matrix , and let
be the 3x3 identity matrix.
If , then evaluate
.
Explanation
The 3x3 identity matrix is
Both scalar multplication of a matrix and matrix addition are performed elementwise, so
is the first element in the third row of
, which is 3; similarly,
. Therefore,