Matrices - Gujarat Board (GSEB) STD 12 Science Maths Questions

If any matrix has order $m \times n$, then number of elements :

A
m
B
n
✓
mn
D
m - n

Answer: C.

Find value of $x$ in equation $\left[\begin{array}{c}x+y+z \\ x+z \\ y+z\end{array}\right]=\left[\begin{array}{l}9 \\ 5 \\ 7\end{array}\right]$

A
$3$
B
$4$
C
$5$
✓
$2$

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark

If $A=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ two matrix, then find AB ?

✓
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
B
$\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right]$
C
$\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$
D
$\left[\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right]$

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark

Two matrix $P =\left[\begin{array}{cc}3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right]$ and $Q ^{ T }=\left[\begin{array}{rrr}-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right]$, Find $P-Q$ :

✓
$\left[\begin{array}{cc}2 & 3 \\ -3 & 0 \\ 0 & 3\end{array}\right]$
B
$\left[\begin{array}{cc}4 & 3 \\ -3 & 0 \\ -1 & -2\end{array}\right]$
C
$\left[\begin{array}{cc}4 & 3 \\ 0 & -3 \\ -1 & -2\end{array}\right]$
D
$\left[\begin{array}{cc}2 & 3 \\ 0 & -3 \\ 0 & -3\end{array}\right]$

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark

If $\left[\begin{array}{cc}3 c+6 & a-d \\ a+d & 2-3 b\end{array}\right]=\left[\begin{array}{cc}12 & 2 \\ -8 & -4\end{array}\right]$ then find $a b-c d$ :

✓
4
B
16
C
-4
D
-16

Answer: A.

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Q 62 Marks Questions2 Marks

If A, B has any two symmetric matrix. Then prove that $A B + B A$ will be a symmetric matrix.

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Q 73 Marks Question3 Marks

In $\left[\begin{array}{cc}x+y & 2 \\ 5+z & x y\end{array}\right]=\left[\begin{array}{ll}6 & 2 \\ 5 & 8\end{array}\right]$ find the value of $x, y, z ?$

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Q 85 Marks Questions5 Marks

A and B has two families. Family A has 4 male, 6 female and 2 children and family B has 2 male, 2 female and 4 children. Every male, female and children has suggested to give respectively 2400, 1900 and 1800 calories per day and 45,55 and 33 gm. protein also. From this informa tion prepare a matrix. Using multiplication of matrix, find the total quantity of calorie and protein for every family.

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Q 9Fill In The Blanks[1 Marks ]1 Mark

If $A =\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$ and $B =\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$, then $A - B =$ ________

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Q 10Fill In The Blanks[1 Marks ]1 Mark

Additive inverse of matrix $\left[\begin{array}{rr}-1 & 2 \\ 0 & -4 \\ 3 & 1\end{array}\right]$ is ________

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Q 11Fill In The Blanks[1 Marks ]1 Mark

If $A+B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $A-2 B=\left[\begin{array}{cc}-1 & 1 \\ 0 & -1\end{array}\right]$, then $A$ $=$ _______

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Q 12Fill In The Blanks[1 Marks ]1 Mark

If $A =\left[\begin{array}{ccc}0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0\end{array}\right]$ has a skew symmetric matrix, then value of $(a+b+c)^2$ ________

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Q 13Fill In The Blanks[1 Marks ]1 Mark

If $\left[\begin{array}{lll}3 & -2 & 0\end{array}\right]\left[\begin{array}{c}2 \\ k \\ -5\end{array}\right]=0$, then value of $k$ is _________

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Q 14Answer the question [ 4 mark question ]4 Marks

If $A=\left[\begin{array}{lll}1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1\end{array}\right]$ and $A^2-4 A=k I_3$ then find the value of $k$. Here $I_3$ has a order of $3 \times 3$ matrix.

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Q 15Answer the question [ 4 mark question ]4 Marks

If $A =\left[\begin{array}{ccc}2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right]$,then find the value of $A ^{ 2 }- 3 A + 2 I$.

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