Matrices and Vectors — Important Questions
ICSE · Class 11 · Artificial Intelligence
65 important questions from Matrices and Vectors for ICSE Class 11 Artificial Intelligence, with answers. Includes multiple choice and multiple correct.
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Important Questions from Matrices and Vectors
Two matrices of order 2 × 3 are added element by element. If A and B are both 2 × 3 matrices, what is the order of A + B?
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2 × 3
When two matrices of order m × n are added, corresponding elements are added and the result is also of order m × n. So A + B has order 2 × 3.
A matrix A is multiplied by a scalar K = 2. If A = [[1,2],[3,-5]], what is 2A?
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[[2,4],[6,-10]]
Scalar multiplication means every element of the matrix is multiplied by the scalar. So 2A = [[2 × 1, 2 × 2],[2 × 3, 2 × (-5)]] = [[2,4],[6,-10]].
For the matrices A = [[2,-3,4],[3,6,-1]] and B = [[2,5],[-1,0],[4,-2]], what is the order of AB?
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2 × 2
Matrix multiplication AB is possible when the number of columns in A equals the number of rows in B. Here A is 2 × 3 and B is 3 × 2, so AB exists and its order is 2 × 2.
Multiply the matrices A = [[2,-3,4],[3,6,-1]] and B = [[2,5],[-1,0],[4,-2]]. What is the entry in the first row, first column of AB?
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23
The first row of A is (2, -3, 4) and the first column of B is (2, -1, 4). Their product is 2 × 2 + (-3) × (-1) + 4 × 4 = 4 + 3 + 16 = 23.
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