Question
If each element of a matrix is zero, then the matrix is:
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper PDF (31-Jan-2021) (Shift 1)
The correct answer is
null
To determine the type of matrix in which each element is zero, let's explore the concept of matrices:
- Null Matrix: A matrix is termed a null matrix or zero matrix if all of its elements are zero. This is the definition that best matches the description given in the question.
- Identity Matrix: An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zero.
- Scalar Matrix: A scalar matrix is a diagonal matrix wherein all the elements on the diagonal are the same non-zero number, and other elements are zero.
- Square Matrix: A matrix is a square matrix if it has the same number of rows and columns. It does not require the elements to be zero.
From the above definitions, it is clear that a matrix where each element is zero is called a null matrix.
The correct answer is: null
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Important Questions from Matrices and Determinants
- Let X be a matrix of order \(3 \times 3\), Y be a matrix of order \(2 \times 3\) and Z be a matrix of order \(3 \times 2\). Which of the following statements are correct?
I. (ZY)X is defined and is a square matrix of order 3.
II. Y(XZ) is defined and is a square matrix of order 2.
III. X(YZ) is not defined.
Select the answer using the code given below. Let \(A\) and \(B\) be matrices of order \(3 \times 3\)., If \(|A| = \frac{1}{2\sqrt{2}}\) and \(|B| = \frac{1}{729}\), then what is the value of \(|2B(\text{adj}(3A))|\)?
- Consider the following statements in respect of two non-singular matrices \(A\) and \(B\) of the same order \(n\):
1. \(\text{adj}(AB) = (\text{adj}A)(\text{adj}B)\)
2. \(\text{adj}(AB) = \text{adj}(BA)\)
3. \((AB)\text{adj}(AB) - |AB|I_n\) is a null matrix of order \(n\)
How many of the above statements are correct? - Consider the following statements in respect of a non-singular matrix \(A\) of order \(n\):
1. \(A(\text{adj}A^T) = A(\text{adj}A)^T\)
2. If \(A^2 = A\), then \(A\) is identity matrix of order \(n\)
3. If \(A^3 = A\), then \(A\) is identity matrix of order \(n\)
Which of the statements given above are correct? - Consider the following statements in respect of a skew-symmetric matrix \(A\) of order \(3\):
1. All diagonal elements are zero.
2. The sum of all the diagonal elements of the matrix is zero.
3. \(A\) is orthogonal matrix.
Which of the statements given above are correct?
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