This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Simplify the following
Possible Answers: Correct answer: 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 .
Possible Answers: Correct answer: 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,
Define matrix , and let be the 3x3 identity matrix.
If , then evaluate .
Possible Answers: Correct answer: 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,
The correct answer is not among the other responses.
Correct answer: Explanation :Scalar multplication of a matrix is done elementwise, so
is the first element in the second row of , which is 5, so
The correct answer is not among the other responses.
Correct answer: 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.
Possible Answers:The correct answer is not given among the other responses.
Correct answer: 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
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