H13-311_V3.5 · Question #311
A scalar k is multiplied by matrix A equal to k and each of the numbers in A is multiplied.
The correct answer is A. True. Multiplying a scalar k by matrix A means every element in A is multiplied by k - this is the definition of scalar multiplication, making the statement True (A). For example, if k = 3 and A = [[1, 2], [3, 4]], then kA = [[3, 6], [9, 12]], confirming each entry is scaled by k…
Question
A scalar k is multiplied by matrix A equal to k and each of the numbers in A is multiplied.
Options
- ATrue
- BFalse
How the community answered
(31 responses)- A74% (23)
- B26% (8)
Explanation
Multiplying a scalar k by matrix A means every element in A is multiplied by k - this is the definition of scalar multiplication, making the statement True (A). For example, if k = 3 and A = [[1, 2], [3, 4]], then kA = [[3, 6], [9, 12]], confirming each entry is scaled by k. Option B (False) is incorrect because scalar multiplication does not selectively apply to some entries or only affect the matrix's determinant - it uniformly scales all elements.
Memory tip: Think of the scalar as a "volume knob" - turning it up or down changes every number in the matrix by the same factor, no exceptions.
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