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Indian Navy INET Algebra — practice questions

Explore 47 free Algebra questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra questions and exercises with answers

Showing questions 1–30 of 47.

A square matrix $A$ is called **idempotent** if:Read the answer and worked solution →A square matrix $A$ satisfies $A^T A = I$. Such a matrix is called:Read the answer and worked solution →The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:Read the answer and worked solution →What are the coordinates of the origin?Read the answer and worked solution →Are the points A(1, 1), B(2, 3), C(3, 5) collinear?Read 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

A square matrix $A$ is called **idempotent** if:

  1. $A^2 = I$
  2. $A^2 = A$
  3. $A^2 = 0$
  4. $A^T = A^{-1}$
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Correct answer: B. $A^2 = A$

**Idempotent:** $A^2 = A$. The identity matrix and the zero matrix are trivial examples. Projection matrices in linear algebra are non-trivial examples. Option A defines an involution (e.g. reflection) option C defines a nilpotent of index 2 option D defines an orthogonal matrix.

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A square matrix $A$ satisfies $A^T A = I$. Such a matrix is called:

  1. Symmetric
  2. Skew-symmetric
  3. Orthogonal
  4. Nilpotent
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Correct answer: C. Orthogonal

An orthogonal matrix satisfies $A^T A = A A^T = I$, equivalently $A^{-1} = A^T$. Its rows (and columns) form an orthonormal set. Rotation and reflection matrices in $\mathbb{R}^n$ are orthogonal. $|A|$ for an orthogonal matrix is always $\pm 1$.

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The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:

  1. (6, 10)
  2. (1, 2)
  3. (2, 4)
  4. (3, 5)
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Correct answer: D. (3, 5)

((2+4)/2, (3+7)/2) = (3,5).

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