KCET · Maths · Matrices
Let X be a matrix of order \(2 \times n\) and Z be a matrix of order \(2 \times p\). If \(n = p\), then the order of the matrix \(8X - 9Z\) is:
- A \(2 \times n\)
- B \(p \times 2\)
- C \(n \times 3\)
- D \(p \times n\)
Answer & Solution
Correct Answer
(A) \(2 \times n\)
Step-by-step Solution
Detailed explanation
The order of matrix \(X\) is \(2 \times n\).
The order of matrix \(Z\) is \(2 \times p\).
Since \(n = p\), the order of matrix \(Z\) can be written as \(2 \times n\).
Scalar multiplication does not change the order of a matrix, so the order of \(8X\) is \(2 \times n\) and the order of \(9Z\) is \(2 \times n\).
Matrix addition or subtraction is defined only for matrices of the same order, and the resulting matrix has the same order.
Thus, the order of the matrix \(8X - 9Z\) is \(2 \times n\).
Answer: \(2 \times n\)
The order of matrix \(Z\) is \(2 \times p\).
Since \(n = p\), the order of matrix \(Z\) can be written as \(2 \times n\).
Scalar multiplication does not change the order of a matrix, so the order of \(8X\) is \(2 \times n\) and the order of \(9Z\) is \(2 \times n\).
Matrix addition or subtraction is defined only for matrices of the same order, and the resulting matrix has the same order.
Thus, the order of the matrix \(8X - 9Z\) is \(2 \times n\).
Answer: \(2 \times n\)
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