alleryStart learning →Rank of the zero matrix:
- 1
- 0
- n
- Variable
Show answer and solution
Correct answer: B. 0
Rank is the number of linearly independent rows (or cols).
For the zero matrix, all rows are zero (no linear independence), so rank = 0.
Indian Navy 10+2 B.Tech Cadet Matrices — practice questions
Explore 30 free Matrices questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Matrices with Quill →Matrices questions and exercises with answers
Showing questions 1–30 of 30.
Rank of the zero matrix:Read the answer and worked solution →In a diagonal matrix, all the non-diagonal elements are:Read the answer and worked solution →The transpose of $A^T$ is:Read the answer and worked solution →For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:Read the answer and worked solution →Order the steps to find the inverse of a 2×2 matrixRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Special square matricesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →
Worked practice questions
In a diagonal matrix, all the non-diagonal elements are:
- equal
- one
- zero
- non-zero
Show answer and solution
Correct answer: C. zero
A diagonal matrix has all off-diagonal entries equal to zero.
The transpose of $A^T$ is:
- $A$, since transposing twice returns the original on chart
- $A^{-1}$, the inverse of the matrix on the school chart
- $-A$, the negative of the original matrix here always
- $2A$, twice the matrix value on the school chart here
Show answer and solution
Correct answer: A. $A$, since transposing twice returns the original on chart
$(A^T)^T = A$, transposing twice returns the original.
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