Algebra — Important Questions
CBSE · Class 12 · Applied Mathematics
47 important questions from Algebra for CBSE Class 12 Applied Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Algebra
Which of the following matrices are diagonal matrices?
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[2 0; 0 3], [5 0 0; 0 -1 0; 0 0 2]
A diagonal matrix has all non-diagonal elements as zero. Options 1 and 3 satisfy this condition as all elements except those on the main diagonal are zero.
If A = [1 2; 3 4], find A².
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[7 10; 15 22]
A² = A × A. Using matrix multiplication: [1 2; 3 4] × [1 2; 3 4] = [1×1+2×3 1×2+2×4; 3×1+4×3 3×2+4×4] = [7 10; 15 22].
What is the transpose of matrix B = [1 3 5; 2 4 6]?
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[1 2; 3 4; 5 6]
The transpose of a matrix is obtained by interchanging rows and columns. B^T converts the 2×3 matrix to a 3×2 matrix where row 1 becomes column 1, etc.
Which type of matrix is [1 0 0; 0 1 0; 0 0 1]?
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Identity matrix
An identity matrix has 1s on the main diagonal and 0s elsewhere. This 3×3 matrix has exactly this pattern, making it the identity matrix I₃.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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