Solve the following system of linear equations using matrix method:
$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 9$
$\frac{2}{x} + \frac{5}{y} + \frac{7}{z} = 52$
$\frac{2}{x} + \frac{1}{y} - \frac{1}{z} = 0$
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Matrices - ISC Class 12 Mathematics Questions with Answers, Page 3
50 past-paper questions on Matrices from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 41-50 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Show that $(A + A')$ is symmetric matrix, if $A = \begin{pmatrix} 2 & 4 \\\\ 3 & 5 \end{pmatrix}$.
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If $A = \begin{pmatrix} 5 & a \\ b & 0 \end{pmatrix}$ and $A$ is a symmetric matrix, show that $a = b$.
Given: $A = \begin{pmatrix} 5 & a \\ b & 0 \end{pmatrix}$ and $A$ is a symmetric matrix
To show: $a = b$
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Evaluate $\begin{pmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{pmatrix} \begin{pmatrix} -1 & -5 & -1 \\ -8 & -6 & 9 \\ -10 & 1 & 7 \end{pmatrix}$.
Hence, solve the system of equations:
$3x - 2y + 3z = 8$
$2x + y - z = 1$
$4x - 3y + 2z = 4$
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Using elementary transformations, find the inverse of the matrix:
$\begin{pmatrix} 1 & 3 & -2 \\ -3 & 0 & -1 \\ 2 & 1 & 0 \end{pmatrix}$
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Using matrices, solve the following system of equations:
$2x - 3y + 5z = 11$
$3x + 2y - 4z = -5$
$x + y - 2z = -3$
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Using elementary transformation, find the inverse of the matrix:
$\begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{pmatrix}$
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Find the value of $k$ if $M = \begin{pmatrix} 1 & 2 \\ 2 & 3 \end{pmatrix}$ and $M^2 - kM - I_2 = 0$.
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Given that: $A = \begin{pmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{pmatrix}$, find $AB$.
Using this result, solve the following system of equation:
$x - y = 3$, $2x + 3y + 4z = 17$ and $y + 2z = 7$
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If the matrix $\begin{pmatrix} 6 & -x^2 \\ 2x - 15 & 10 \end{pmatrix}$ is symmetric, find the value of $x$.
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