Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$

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Linear Algebra

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How GATE tests Linear Algebra

Linear Algebra in GATE CS is consistently tested across fundamental properties of matrices, systems of linear equations, and spectral theory (eigenvalues and eigenvectors). Questions heavily leverage algebraic identities such as trace-sum, determinant-product relations, rank-nullity theorem, and structural properties like orthogonality of symmetric matrices and LU decomposition. Problems frequently appear as 1-mark and 2-mark conceptual MCQs/MSQs or direct numerical computation NATs.

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Engineering Mathematics · Linear Algebra

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GATE CSE 2015 Set 1 Q36 · MCQ · 2 marks

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$

Select an option to check

Key concept

Linear Algebra

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Linear Algebra

Full Linear Algebra guide →

More on Linear Algebra

All 46 questions on Linear Algebra →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$

Step-by-step verified solution

Check you can still solve Linear Algebra under a clock

More from GATE CSE 2015 Set 1

More on Linear Algebra

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$

Step-by-step verified solution

Check you can still solve Linear Algebra under a clock

More from GATE CSE 2015 Set 1

More on Linear Algebra

Consider the following 2×22 \times 22×2 matrix AAA where two elements are unknown and are marked by aaa and bbb. The eigenvalues of this matrix are -1 and 7. What are the values of aaa and bbb? A=(14ba)A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}A=(1b​4a​)

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Check you can still solve Linear Algebra under a clock

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Consider the following 2×22 \times 22×2 matrix AAA where two elements are unknown and are marked by aaa and bbb. The eigenvalues of this matrix are -1 and 7. What are the values of aaa and bbb? A=(14ba)A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}A=(1b​4a​)

Step-by-step verified solution

Check you can still solve Linear Algebra under a clock

More from GATE CSE 2015 Set 1

More on Linear Algebra

Share this solution

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$

Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$ . The eigenvalues of this matrix are -1 and 7. What are the values of $a$ and $b$ ? $A = \begin{pmatrix} 1 & 4 \\ b & a \end{pmatrix}$