alleryStart learning →tan(45°) equals:
- ∞
- 0
- 1
- √3
Show answer and solution
Correct answer: C. 1
We have tan(45°) = sin(45°)/cos(45°).
That is tan(45°) = (1/√2)/(1/√2).
So tan(45°) = 1.
KCET Matrices and Determinants — practice questions
Explore 95 free Matrices and Determinants questions in KCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 95.
tan(45°) equals:Read the answer and worked solution →A matrix is:Read the answer and worked solution →Identity matrix I has:Read the answer and worked solution →For matrix multiplication AB to be defined:Read the answer and worked solution →Determinant of 2×2 matrix [[a, b], [c, d]]:Read the answer and worked solution →Determinant of triangular (upper or lower) matrix:Read the answer and worked solution →A matrix is invertible iff:Read the answer and worked solution →For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =Read the answer and worked solution →Transpose of [[1,2,3],[4,5,6]] is:Read the answer and worked solution →For matrices A, B (square, same size): (AB)^T =Read the answer and worked solution →A matrix is symmetric if:Read the answer and worked solution →A matrix is skew-symmetric if:Read the answer and worked solution →Determinant of identity matrix I_n:Read the answer and worked solution →Determinant: if two rows are equal, det =Read the answer and worked solution →For matrix A with |A| = 5 and A is 3×3, |2A| =Read the answer and worked solution →For matrix A and its adjugate adj(A): A × adj(A) =Read the answer and worked solution →For non-singular A and scalar k: |k A^(-1)| = (A is n × n)Read the answer and worked solution →Solve: x + y + z = 6, 2x + y - z = 1, x - y + z = 2. Determinant of coefficient matrix:Read the answer and worked solution →If A is orthogonal (A A^T = I), then |A| =Read the answer and worked solution →For A = [[3, 1], [2, 4]], characteristic polynomial:Read the answer and worked solution →Eigenvalues of A = [[3,1],[2,4]]:Read the answer and worked solution →For matrix A, rank(A) + nullity(A) =Read the answer and worked solution →For A symmetric n×n matrix, all eigenvalues are:Read the answer and worked solution →Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]:Read the answer and worked solution →System of equations Ax = b has unique solution iff:Read the answer and worked solution →For 3×3 matrix with rows R₁, R₂, R₃ = R₁ + 2R₂. Determinant =Read the answer and worked solution →If A is 3×3 with |A| = -2, then |adj(A)| =Read the answer and worked solution →Product of eigenvalues of square matrix A =Read the answer and worked solution →SAT · Mathematics · Trig Ratios (SOHCAHTOA)Read the answer and worked solution →SAT · Mathematics · Trig Identities — T/FRead the answer and worked solution →
Worked practice questions
A matrix is:
- A vector
- A rectangular array of numbers arranged in rows and columns
- A single number
- A point
Show answer and solution
Correct answer: B. A rectangular array of numbers arranged in rows and columns
**Matrix:** rectangular array of numbers in m rows × n columns.
**Notation:** A_(ij) = element in row i, column j. Size denoted m × n.
Identity matrix I has:
- 1s on diagonal, 0s elsewhere; AI = A for any A
- All 1s except diagonal
- All zeros
- All 1s
Show answer and solution
Correct answer: A. 1s on diagonal, 0s elsewhere; AI = A for any A
Identity matrix I_n: square n × n with 1's on diagonal, 0's off-diagonal.
**For any compatible A:** AI = A = IA.
Multiplicative identity for matrices.
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