What is {bmatrix} x & y & z {bmatrix} {bmatrix} a & h & g \\ h & b & f \\ g & f & c {bmatrix} equal to?

Correct Answer is : [ax + hy + gz hx + by + fz gx + fy + cz]

[ax + hy + gz h + b + f g + f + c]

≤ft[ {{array}{ccc} {{a}}&{{h}}&{{g}}\\ {{{hx}}}&{{{by}}}&{{{fz}}}\\ {{g}}&{{f}}&{{c}} {array}} ]

≤ft[ {array}{c} {ax} + {hy} + {gz} \\ {hx} + {by} + {fz} \\ {gx} + {fy} + {cs} {array} ]

[ax + hy + gz hx + by + fz gx + fy + cz]

Correct Answer is : [ax + hy + gz hx + by + fz gx + fy + cz]

Test Index

UPSC NDA 2 2016 Mathematics Solved Paper

Question : 7 of 120

Marks: +1, -0

What is

\begin{bmatrix} x & y & z \end{bmatrix} \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}

equal to?

[ax + hy + gz h + b + f g + f + c]
$\left[ {\begin{array}{ccc} {\rm{a}}&{\rm{h}}&{\rm{g}}\\ {{\rm{hx}}}&{{\rm{by}}}&{{\rm{fz}}}\\ {\rm{g}}&{\rm{f}}&{\rm{c}} \end{array}} \right]$
$\left[ \begin{array}{c} \mathrm{ax} + \mathrm{hy} + \mathrm{gz} \\ \mathrm{hx} + \mathrm{by} + \mathrm{fz} \\ \mathrm{gx} + \mathrm{fy} + \mathrm{cs} \end{array} \right]$
[ax + hy + gz hx + by + fz gx + fy + cz]

Solution:

Concept:

Multiplying a

1 \times 3

row vector with a

3 \times 3

matrix yields a

1 \times 3

row vector.

Explanation:

We compute the product

[x \quad y \quad z] \begin{bmatrix} a & h & g \\ h & b & f \\ g & f & c \end{bmatrix}

by standard row‑by‑column multiplication.

The first entry is

x \cdot a + y \cdot h + z \cdot g = ax + hy + gz

The second entry is

x \cdot h + y \cdot b + z \cdot f = hx + by + fz

The third entry is

x \cdot g + y \cdot f + z \cdot c = gx + fy + cz

Thus the product equals

[ax + hy + gz \quad hx + by + fz \quad gx + fy + cz]

Answer:

Option D:

[ax + hy + gz \quad hx + by + fz \quad gx + fy + cz]

Go to Question:

Prev Question

Next Question